One side of a rectangle is 3 feet shorter than twice the other side find the sides if the area is 209 ft.²

Answer:

124 miles

Step-by-step explanation:

Since he has a budget of $54.00, we first deduct the fixed charge of $29.2

Money for the miles will be 54-29.2=$24.8

Cost per mile is $0.2

[tex]Miles=\frac {24.8}{0.2}=124 miles[/tex]

Therefore, Mike is limited to travel 124 miles with the car on hire

Answer:

The first one.

Step-by-step explanation:

The third and fourth ones can't be right because at when the line takes its first curve (just before .25 hours) it doesn't keep increasing in height, and she walked during that time.

The second one can't be right because when she started out she wasn't immediately between 1.25 and 1.5 miles.

That leaves only the first one.

The graph for the given situation is required.

The correct option is the first graph.

Let us convert the minutes to hour since the graph is shown in hours.

[tex]\dfrac{13}{60}=0.2167\ \text{hours}[/tex]

[tex]\dfrac{17}{60}=0.2833\ \text{hours}[/tex]

Whenever a line in a graph has an angle with the [tex]x[/tex] axis then there is a change of the [tex]y[/tex] axis with respect to change in [tex]x[/tex] axis.

That means slope

[tex]m=\dfrac{\Delta y}{\Delta x}[/tex]

Here, the slope of an angled line will be

[tex]m=\dfrac{\text{Change in distance}}{\text{Change in time}}=\text{Speed}[/tex]

The slope here indicates constant speed.

From 0 to 0.2167 hours she ran at constant speed.

From 0.2167 to [tex]0.2167+0.2833=0.5[/tex] hours she walked

From 0.5 hours to [tex]0.5+0.2167=0.7167[/tex] hours she ran.

From 0.7167 hours to [tex]0.7167+0.2833=1[/tex] hour she sat and stretched.

The slope or angle will be more for the running sections compared to the walking sections as running is faster than walking.

And the graph will always be going up.

At the end when she is not moving the line will be a horizontal line because her position is not changing.

So, the correct option is the first graph.

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Answer:

-$4

Step-by-step explanation:

The expected payback formula is the sum of probability multiply the value

E(x) = p(x1)*x1 + p(x2)*x2 + .....

In this case, we have two possibility of payback

1) winning

The payback is $400 -$8 = $392

x1 = 392

The probability of winning is one out of 100 (since the choices are 0 to 99)

p(x1) = 1/100

2. Losing

The payback is -$8 since the person didn't win anything is loose

x2 = -8

Since there is only one winning number, the other 99 numbers are loosing numbers

p(x2) = 99/100

Therefore expected payback is

E(x) = p(x1)*x1 + p(x2)*x2

= (1/100)*392 + (99/100)*(-8)

= -400/100

= -$4

The expected payback for a game in which you bet $8 on any number from 0 to 99, and win $400 if your number comes up, is -$4.00, indicating an average loss of $4.00 per game.

In this probability problem, you are betting $8 on a number from 0 to 99. This means there are 100 possible outcomes, each equally likely if the game is fair. Your profit if you win is $400. Since there's a 1 in 100 chance of winning, we can calculate the expected return as follows:

Expected Return = Probability of winning * Payoff when winning = (1/100) * $400 = $4.00

However, since you are always paying $8 to play the game, in expectation you are losing money in every game. The expected payback from this game is hence $4-$8=-$4.00 and not $48.00. In other words, we can anticipate losing $4.00 on average every time we play this game.

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Answer:

par value of the TIPS is $1034.05

Step-by-step explanation:

Given:

-  original reference CPI = 182.1

- current CPI = 188.3

Assume face value of tips = $1000

par value of the TIPS = [tex]face\ value\ of\ tips\times \frac{current\ CPI}{original\ reference\ CPI}[/tex]

par value of the TIPS = [tex]1000\times \frac{188.3}{182.1}\approx $1034.05[/tex]

Final answer:

The par value of a TIPS adjusts with the CPI's inflation rate. To find the adjusted par value of a 4.15% TIPS, multiply the original par value by 1 plus the inflation rate, which is determined by the percentage increase from the original to the current CPI.

Explanation:

A student asked about the par value of a Treasury Inflation-Protected Security (TIPS) given an original reference Consumer Price Index (CPI) of 182.1 and a current CPI of 188.3. The par value of TIPS adjusts with inflation to protect investors, with the adjustment based on the change in the CPI.

First, we need to calculate the percentage increase in the CPI by using the formula:

(Current CPI - Original CPI) ÷ Original CPI x 100%.

Plugging in the given CPI values:

(188.3 - 182.1) ÷ 182.1 = 0.0340 or 3.40%

This percentage tells us how much the CPI has increased since the TIPS was issued. To find the adjusted par value, you would multiply the original par value of the TIPS (which is typically $1,000) by 1 plus the inflation rate. Since we do not have the original par value, we can only provide the formula for its calculation.

The adjusted par value would be:

Original Par Value x (1 + Inflation Rate).

Assumption:

Something is missing in question. If we see deeply it is apparent that there is some issue with option b i.e. B) 8 − 4x 10 = 4 + 2x we assume that the questioner want to type B) 8-4x^10 = 4 + 2x.

Answer:

The correct answer is B) 8-4x^10 = 4 + 2x.

Step-by-step explanation:

All equations given is the question can be solve easily to determine the value of x. However if we solve equation mentioned in option b we cannot  get single answer easily.

For example value of x in eq given in option A

15x + 123 = 5x+4

1oX = -119

 X = -119/10

Answer:

The answer is d

Step-by-step explanation:

i just did it lol

Answer:

The height of the aquarium is [tex]33.75\ in[/tex]

Step-by-step explanation:

Remember that

[tex]1\ gal=231\ in^3[/tex]

[tex]1\ ft=12\ in[/tex]

we know that

The volume of a rectangular prism is equal to

[tex]V=LWH[/tex]

In this problem we have

[tex]V=1,000\ gal=1,000(231)=231,000\ in^3[/tex]

so

[tex]231,000=LWH[/tex] ----> equation A

[tex]L=W+1(12)[/tex] ---> [tex]W=L-12[/tex]  --->equation B (convert ft to in)

[tex]H=L-4.6(12)[/tex]--->[tex]H=L-55.2[/tex] ---> equation C (convert ft to in)  

substitute equation B and equation C in equation A

[tex]231,000=L(L-12)(L-55.2)[/tex]

solve for L

Apply distributive property

[tex]231,000=(L^2-12L)(L-55.2)[/tex]

[tex]231,000=L^3-55.2L^2-12L^2+662.4L[/tex]

[tex]L^3-67.2L^2+662.4L-231,000=0[/tex]

Solve the cubic equation by graphing

using a graphing tool

The solution is L=88.95 in

see the attached figure

Find the height of the aquarium H

[tex]H=L-55.2[/tex]

substitute the value of L

[tex]H=88.95-55.2=33.75\ in[/tex]

Find the value of W  

[tex]W=88.95-12=76.95\ in[/tex]

Answer:

0.6

Step-by-step explanation:

The the exponent is positive , move it 3 times to the right.

If it was a negative exponent , you would move it to the left.

Answer:

30%

Step-by-step explanation:

Use formula to find percent decrease

[tex]\text{Percent Decrease}=\dfrac{\text{Old Value}-\text{New Value}}{\text{Old Value}}\cdot 100\%[/tex]

In your case,

Old Value = 2.5 pounds

New Value = 1.75 pounds

Hence,

[tex]\text{Percent Decrease}=\dfrac{2.5-1.75}{2.5}\cdot 100\%\\ \\=\dfrac{0.75}{2.5}\cdot 100\%\\ \\=\dfrac{75}{250}\cdot 100\%\\ \\=\dfrac{3}{10}\cdot 100\%\\ \\=30\%[/tex]

Answer:

c a multiple of 13

Step-by-step explanation:

The resulting number will be a multiple of 13 if 13 is added 101 times option (C) A multiple of 13 is correct.

A number is a mathematical entity that can be used to count, measure, or name things. For example, 1, 2, 56, etc. are the numbers.

It is given that:

if 13 is added 101 times:

The arithmetic operation can be defined as the operation in which we do the addition of numbers, subtraction, multiplication, and division. It has a basic four operators that is +, -, ×, and ÷.

= 13 + 13 + 13 + 13 ...... 101 times

Sequence can be defined as the systematic way of representing the data that follows a certain rule of arithmetic.

= 101×(13)

Thus, the resulting number will be a multiple of 13 if 13 is added 101 times option (C) A multiple of 13 is correct.

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Answer:

[tex]f^{-1}(x)=\frac{x}{6}+\frac{2}{3}[/tex]

Step-by-step explanation:

Given function.

[tex]f(x)=6x-4[/tex]

To find the inverse function [tex]f^{-1}(x)[/tex]

Step 1:

Replace [tex]f(x)[/tex] with[tex]y[/tex] in the function.

[tex]y=6x-4[/tex]

Step 2:

Interchange [tex]y[/tex] with [tex]x[/tex] in the equation.

[tex]x=6y-4[/tex]

Step 3:

Solve for [tex]y[/tex].

We have [tex]x=6y-4[/tex]

Adding 4 to both sides,

[tex]x+4=6y-4+4[/tex]

[tex]x+4=6y[/tex]

Dividing each term by 6 to isolate [tex]y[/tex]

[tex]\frac{x}{6}+\frac{4}{6}=\frac{6y}{6}[/tex]

[tex]\frac{x}{6}+\frac{4}{6}=y[/tex]

Simplifying fractions by dividing the numerator and denominator by  their GCF.

[tex]\frac{x}{6}+\frac{4\div 2}{6\div 2}=y[/tex]

[tex]\frac{x}{6}+\frac{2}{3}=y[/tex]

Thus the equation of [tex]y[/tex] is:

[tex]y=\frac{x}{6}+\frac{2}{3}[/tex]

Step 4:

Replace [tex]y[/tex] with [tex]f^{-1}(x)[/tex]

[tex]f^{-1}(x)=\frac{x}{6}+\frac{2}{3}[/tex] (Answer)

Thus, we have the inverse function

Answer:  0.85

Step-by-step explanation:

step 1   0.3572928 / 0.419

             count the number of figures yo have after the decimal  point.

After counting , multiply both the numerator and the denominator

10000000 to make the whole expression a whole number for easy division.

   we now      0.3572928                 10000000

                     ------------------       x        ---------------

                         0.419                         10000000

           =         3572928

                    ----------------

                      4190000

         =           0.8527

        Now to two decimal places

              = 0.85

Answer:

No

Step-by-step explanation:

The square root of 34 does not multiply by itself

Yes, the square foot of 34 is a rational number

Any fraction with non-zero denominators is a rational number. Some of the examples of rational numbers are 1/2, 1/5, 3/4, and so on.

square root, in mathematics, a factor of a number that, when multiplied by itself, gives the original number. For example √25 = 5 i.e 5 × 5 = 25

The square root of 34 is of a value

√34 = 5.381

This value can be converted into fraction

= 5381/1000

Therefore we can say that the square root of 34 is a rational number.

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Answer:

  3. (x, y) = (3, 2)

  6. (x, y) = (10, 4/3)

  9. (x, y) = (-2, -1)

  12. (x, y) = (8, 3)

Step-by-step explanation:

3, 6. See the attachment. 3 is graphed in red/orange. 6 is graphed in blue, purple.

__

9. Use the expression for y in the second equation to substitute for y in the first equation:

  4(3x +5) -x = -2

  12x +20 -x = -2 . . . eliminate parentheses

  11x = -22 . . . . . . . .  subtract 20, collect terms

  x = -2 . . . . . . . . . . . divide by 11

  y = 3(-2) +5 = -1 . . .substitute for x in the second equation

The solution is (x, y) = (-2, -1).

__

12. Subtract 3/4x from the second equation to get an expression for y:

  y = 9 - 3/4x

Substitute that into the first equation:

  3(9 -3/4x) -5/4x = -1

  27 -9/4x -5/4x = -1 . . . . eliminate parentheses

  -14/4x = -28 . . . . . . . . . . collect terms, subtract 27

  x = 8 . . . . . . . . . . . . . . . . multiply by -4/14

  y = 9 -3/4(8) = 3 . . . . . . substitute into the expression for y

The solution is (x, y) = (8, 3).

Answer:

Step-by-step explanation:

h(x) - j(x) => [tex]x^2-(2x^2-5)[/tex]

The negative sign out in front of the set of parenthesis changes the signs of everything inside the parenthesis, so now we have, without parenthesis:

[tex]x^2-2x^2+5[/tex] which simplifies down to

[tex]-x^2+5[/tex]

Answer:

-17/10

Step-by-step explanation:

-4(1/8)-3(2/5)=-4/8-6/5=-20/40-48/40=-68/40=-17/10

Answer: point, line, and plane.

Step-by-step explanation:

Answer:

Hope it helps In Geometry, we have several undefined terms: point, line and plane. From these three undefined terms, all other terms in Geometry can be defined.  A line is defined as something that extends infinitely in either direction but has no width and is one dimensional while a plane extends infinitely in two dimensions.

Step-by-step explanation:

Step-by-step explanation:

Given the equation

[tex]3x^3\:+10x^2-x-12=0[/tex]

Steps

[tex]3x^3+10x^2-x-12[/tex]

Rational Root Theorem definition

[tex]\mathrm{For\:a\:polynomial\:equation\:with\:integer\:coefficients:\quad }a_nx^n+a_{n-1}x^{n-1}+\ldots +a_0[/tex]

[tex]\mathrm{If\:}a_0\mathrm{\:and\:}a_n\mathrm{\:are\:integers,\:then\:if\:there\:is\:a\:rational\:solution}[/tex]

[tex]it\:could\:be\:found\:by\:checking\:all\:the\:numbers\:produced\:for\:\pm \frac{dividers\:of\:a_0}{dividers\:of\:a_n}[/tex]

[tex]a_0=12,\:\quad a_n=3[/tex]

[tex]\mathrm{The\:dividers\:of\:}a_0:\quad 1,\:2,\:3,\:4,\:6,\:12,\:\quad \mathrm{The\:dividers\:of\:}a_n:\quad 1,\:3[/tex]

[tex]\mathrm{The\:following\:rational\:numbers\:are\:candidate\:roots:}\quad \pm \frac{1,\:2,\:3,\:4,\:6,\:12}{1,\:3}[/tex]

Plugging x = -1 is False

[tex]3\left(-1\right)^3+10\left(-1\right)^2-\left(-1\right)-12=0[/tex]

[tex]-4=0[/tex]    ∵L.H.S ≠ R.H.S

Plugging x = 1 is True

[tex]3\cdot \:1^3+10\cdot \:1^2-1-12=0[/tex]

[tex]0=0[/tex]      ∵ L.H.S = R.H.S

Similarly,

x = -2 does not satisfy the equation [tex]3x^3\:+10x^2-x-12=0[/tex].

x = 2 does not satisfy the equation [tex]3x^3\:+10x^2-x-12=0[/tex].

x = -3 satisfies the equation [tex]3x^3\:+10x^2-x-12=0[/tex].

As

[tex]3\left(-3\right)^3+10\left(-3\right)^2-\left(-3\right)-12=0[/tex]

[tex]0=0[/tex]       ∵ L.H.S = R.H.S

x = 3 does not satisfy the equation [tex]3x^3\:+10x^2-x-12=0[/tex].

x = 4 does not satisfy the equation [tex]3x^3\:+10x^2-x-12=0[/tex].

x = -4 does not satisfy the equation [tex]3x^3\:+10x^2-x-12=0[/tex].

x = 6 does not satisfy the equation [tex]3x^3\:+10x^2-x-12=0[/tex].

x = -6 does not satisfy the equation [tex]3x^3\:+10x^2-x-12=0[/tex].

x = -12 does not satisfy the equation [tex]3x^3\:+10x^2-x-12=0[/tex].

x = 12 does not satisfy the equation [tex]3x^3\:+10x^2-x-12=0[/tex].

x = -1/3 does not satisfy the equation [tex]3x^3\:+10x^2-x-12=0[/tex].

x = 1/3 does not satisfy the equation [tex]3x^3\:+10x^2-x-12=0[/tex].

x = -2/3 does not satisfy the equation [tex]3x^3\:+10x^2-x-12=0[/tex].

x = 2/3 does not satisfy the equation [tex]3x^3\:+10x^2-x-12=0[/tex].

x = -4/3 satisfies the equation [tex]3x^3\:+10x^2-x-12=0[/tex].

As

[tex]3\left(-\frac{4}{3}\right)^3+10\left(-\frac{4}{3}\right)^2-\left(-\frac{4}{3}\right)-12=0[/tex]      ∵ L.H.S = R.H.S  

x = 4/3 does not satisfy the equation [tex]3x^3\:+10x^2-x-12=0[/tex].

x = -2 does not satisfy the equation [tex]3x^3\:+10x^2-x-12=0[/tex].

x = 2 does not satisfy the equation [tex]3x^3\:+10x^2-x-12=0[/tex].

x = -4 does not satisfy the equation [tex]3x^3\:+10x^2-x-12=0[/tex].

x = 4 does not satisfy the equation [tex]3x^3\:+10x^2-x-12=0[/tex].

Hence, out of all the mentioned rational roots of the equation [tex]3x^3\:+10x^2-x-12=0[/tex], the rational roots which validate the equation are [tex]x=-\frac{4}{3},\:x=1,\:x=-3[/tex].

Keywords: rational roots, rational root theorem

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Answer:

[tex]S=42000*\sum_{i=0}^{n}0.02^n[/tex]

Step-by-step explanation:

The salary per year is the combination of the $42000 per year (constant) plus the 2% rise per year. So the ecuation is:

Firt year [tex]S=(42000 + 0.02*42000)[/tex]

Second year [tex]S=(42000 + 0.02*42000)+0.02*(42000 + 0.2*42000)[/tex]

Generalizing:

[tex]S=42000*\sum_{i=0}^{n}0.02^n[/tex]

Final answer:

The equation that represents Giovanna's current situation is Current Salary = $42,840.

Explanation:

The equation that represents Giovanna's current situation can be determined by using the formula for calculating annual salary with a percentage increase.

The formula is:
Current Salary = Initial Salary + (Percentage Increase * Initial Salary)

Using this formula, we can substitute the given values:
Initial Salary = $42,000
Percentage Increase = 2% (or 0.02)

Substituting these values into the formula:

Current Salary = $42,000 + (0.02 * $42,000)

Simplifying the equation:

Current Salary = $42,000 + $840

Current Salary = $42,840

Therefore, the equation that represents Giovanna's current situation is:
Current Salary = $42,840

The final concentration of salicylic acid in the ointment is approximately 8.70%.

To calculate the final concentration of salicylic acid in the ointment base, we need to know the total mass of the product after mixing. The final concentration of salicylic acid is expressed as a percentage, which is the mass of salicylic acid divided by the total mass of the product, multiplied by 100.

Let's assume that when you add 8 g of salicylic acid to 84 g of the ointment base, there is no change in the total volume, and the two substances mix completely.

Total mass of the product = Mass of salicylic acid + Mass of ointment base

Total mass = 8 g + 84 g = 92 g

Now, we can calculate the final concentration of salicylic acid:

Final Concentration (%) = (Mass of salicylic acid / Total mass) * 100

Final Concentration (%) = (8 g / 92 g) * 100 ≈ 8.70%

So, the final concentration of salicylic acid in the ointment is approximately 8.70%.

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Answer:

[tex]\large\boxed{16a^6x^4y^2}[/tex]

Step-by-step explanation:

[tex]\text{Use}\\\\(ab)^n=a^nb^n\\\\(a^n)^m=a^{nm}\\=====================\\\\\left(-4x^2ya^3\right)^2=\\\\=(-4)^2(x^2)^2(y)^2(a^3)^2\\\\=(-4)(-4)x^{2\cdot2}y^2a^{3\cdot2}\\\\=16x^4y^2a^6[/tex]

The expression (−4x^2ya^3)^2 written as a monomial in standard form is 16x^4y^2a^6.

To write the given expression, (−4x2ya3)2, as a monomial in standard form, we first need to calculate square ofeach part of the term inside the parentheses. The square of -4 is 16. The rule of exponents states that when raising a power to a power, you multiply the exponents. Therefore, the square of x2 is x4 (since 2*2=4), the square of y is y2, and the square of a3 is a6 (since 3*2=6). Combining these, we find that the expression in standard form is 16x4y2a6.

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Final answer:

The fraction of a 3-gallon container filled with 1/3 gallon of water is 1/9. This is found by dividing the amount of water by the total capacity of the container. It can be represented through multiplication and division, both yielding the result 1/9.

Explanation:

The question asks what fraction of a container is filled if there is 1/3 gallon of water in a 3-gallon container. To represent this situation, we can simply realize that the fraction filled is equal to the amount of water in the container (1/3 gallon) divided by the container's total capacity (3 gallons).

So, 1/9 of the container is filled with water.

To set up a multiplication and division equation to represent the situation:

These representations show how to derive the fraction of the container that is filled using multiplication and division.

Final answer:

The Peace of Augsburg allowed rulers to establish either Lutheranism or Roman Catholicism as the official religion in their lands, giving birth to the principle 'whose realm, their religion' but excluded other religious groups such as Calvinists and Anabaptists.

Explanation:

The religious settlement reached with the Peace of Augsburg in 1555 allowed rulers within the Holy Roman Empire to choose either Lutheranism or Roman Catholicism as the official religion of their territories. This principle, known as cuius regio, eius religio ('whose realm, their religion'), meant that a ruler's subjects were obliged to follow the same religion.

The Peace of Augsburg formally recognized the division between Catholics and Protestants, mainly Lutherans, and ended the religious conflict within the empire at that time. However, other religious groups, such as Calvinists and Anabaptists, were not accommodated, and the agreement failed to resolve underlying tensions leading to future wars, including the devastating Thirty Years' War.

Answer:

Two options for this case will be,

Clockwise rotation : -90°

Anti-Clockwise rotation : +270°

Step-by-step explanation:

If we rotate the triangle clockwise -90° then the vertex will be at (5,0).

Similarly by rotatating it anti-clockwise for +270° it will be at same position

Answer:

C.) D.)

Step-by-step explanation:

Answer:

8X2-38X-380

Step-by-step explanation:

(2x+10)(4x-38)

Expand the brackets.

2X(4X-38)+10(4X-38)

Multiple the inner ones by the outer ones

(2X)(4X)-(38)(2X)+(10)(4X)-(10)(38)

=> 8X2-78X+40X-380

8X2-38X-380

Answer:

8x^2y= 8x^3 - 4x^2

y = x - 1/2

y = (2x - 1)/2

the answer is c

The equilibrium price 'p' is found when setting the supply and demand equations equal to each other and solving for p. Doing so gives us p = 29, which is not available among the provided options, suggesting an error in the question or answer options.

In the given situation, the point of equilibrium occurs when the quantity demanded (D) is equal to the quantity supplied (S). Therefore, we can set the demand equation equal to the supply equation and solve for p.

The equations at the moment are: D = p + 22 and S = 3p - 36.

Setting them equal to each other means setting D and S to the same value, resulting in: p + 22 = 3p – 36.

To solve for p, you first combine like terms, which will give you: 22 + 36 = 3p - p, simplifying that leads to: 58 = 2p.

Finally, to isolate p, divide both sides of the equation by 2: p = 58 / 2 = 29.

However, none of the options includes p = 29, which suggests there might be a typo or error in the provided choices or the equations.

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Answer:

Option C) 24 < x < 54

Step-by-step explanation:

we know that

The Triangle Inequality Theorem states that the sum of any 2 sides of a triangle must be greater than the measure of the third side

Let

x ----> the measure of the third side

Applying the triangle inequality theorem

1) [tex]15+39 > x[/tex]

[tex]54 > x[/tex]

Rewrite

[tex]x < 54\ units[/tex]

2) [tex]x+15> 39[/tex]

[tex]x > 39-15[/tex]

[tex]x > 24\ units[/tex]

therefore

The range of possible measures for the third side is the interval (24,54)

Answer:

7^9

Step-by-step explanation:

When dealing with exponents inside and outside parenthesis with only one term in the parenthesis, you multiply the exponents. By doing this, you get 7^3x3, which is 7^9

Answer:

40353607 or 7^9

Step-by-step explanation:

7 to the third power is 343

343 to the third power is 40353607 :)

But the exponents times each other equal nine. This will be your answer: 7^9