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SAT Math : Exponential Operations

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Example Questions

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Example Question #41 : Exponents

Simplify into base .

32^1*8^4*4^2

Possible Answers:

$2^{21}$

2^7

$2^{20}$

Can't be simplified.

$2^{240}$

Correct answer:

$2^{21}$

Explanation:

We need to get them to bases of . All of those bases derive from bases of but raised to different powers. is the same as 32^1 as anything raised to the first power is the same as its base. 32=2^5 .

Next, 8=2^3 . Since it's raised to the fourth power, let's make a proportion.

$\frac{1}{3}=\frac{4}{x}$ .
The top represents the power of base . The bottom represents the power of base . When we cross-multiply, we have . So $8^4=2^{12}$ .

Finally, is the same as 2^2 . Let's do another proportion.

$\frac{1}{2}=\frac{2}{x}$ .

The top represents the power of base . The bottom represents the power of base .Wen we cross-mulltiply, we get . So 4^2=2^4 .

With the same bases, we can add the exponents.

We have $2^{5+12+4}=2^{21}$ .

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Example Question #41 : Exponents

x^8 can be stated as which of the following?

Possible Answers:

2 and 3

2 only

3 only

1 only

1 and 3

Correct answer:

2 and 3

Explanation:

This will test your knowledge of a specific exponential property: $(x^a)^b = x^{ab}$ . Knowing that, 2 and 3 do come out to x^8 , while 1 comes out to only x^6 .

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Example Question #41 : How To Multiply Exponents

Simplify:

$(x^\frac{1}{2}y^\frac{3}{2})^2$

Possible Answers:

$x^\frac{5}{2}y^\frac{7}{2}$

$x^\frac{3}{2}y^\frac{5}{2}$

$\frac{y^\frac{1}{2}}{x}$

xy^3

Correct answer:

xy^3

Explanation:

When an exponent is raised to the power of another exponent, we multiply the exponents together.

For our x-value, the exponent will be $\frac{1}{2}\cdot 2 =1$

For our y-value, the exponent will be $\frac{3}{2}\cdot 2=3$

Therefore,

$(x^\frac{1}{2}y^\frac{3}{2})^2 = xy^3$

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Example Question #44 : Exponents

Solve for in terms of :

$t ^{- \frac{2}{5}} = h^{10}$

Possible Answers:

$t = \frac{1}{h^{4}}$

$t = \frac{1}{h^{25}}$

$t = \sqrt[4]{h}$

t = 100 h

$t = \sqrt[25]{h}$

Correct answer:

$t = \frac{1}{h^{25}}$

Explanation:

$t ^{- \frac{2}{5}} = h^{10}$

$\left (t ^{- \frac{2}{5}} \right )^{- \frac{5} {2}} =\left ( h^{10} \right )^{- \frac{5} {2}}$

$t ^{- \frac{2}{5} \cdot \left ( - \frac{5} {2} \right )} = h^{10 \cdot \left ( - \frac{5} {2} \right )}$

$t ^{1} = h^{-25 }$

$t = \frac{1}{h^{25}}$

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Example Question #42 : Exponents

Evaluate $6^{18}*6^{24}$

Possible Answers:

$6^{24}$

$6^{42}$

$6^{432}$

$6^{48}$

$6^{36}$

Correct answer:

$6^{42}$

Explanation:

When multiplying exponents of the same base, we just add the exponents and keep the base the same.

$6^{18}*6^{24}=6^{18+24}=6^{42}$

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Example Question #43 : Exponents

Evaluate $7^{-5}*7^{-8}$

Possible Answers:

$7^{16}$

$7^{-10}$

$7^{-12}$

$7^{-13}$

$7^{40}$

Correct answer:

$7^{-13}$

Explanation:

When multiplying exponents of the same base, we just add the exponents and keep the base the same.

$7^{-5}*7^{-8}=7^{-5-8}=7^{-13}$

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Example Question #44 : Exponents

Evaluate 81^8*3^9

Possible Answers:

$243^{72}$

$3^{80}$

$243^{17}$

$3^{41}$

9^9

Correct answer:

$3^{41}$

Explanation:

Although we have different bases, we know that 81=3^4. Therefore we have $(3^4)^8*3^9=3^{32}*3^9=3^{41}$ .

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Example Question #48 : Exponents

Simplify $\frac{x+(3x)^2+(2x)^3}{x}$

Possible Answers:

x+9x^2+8x^3

x+9x+8x^2

1+9x+8x^2

1+6x+6x^2

$\frac{1+9x+8x^2}{x}$

Correct answer:

1+9x+8x^2

Explanation:

Simplify the numerator

$\frac{x+(3x)^2+(2x)^3}{x}=\frac{x+3^2x^2+2^3x^3}{x}=\frac{x+9x^2+8x^3}{x}$

Pull an x out of each term in the numerator

$\frac{x(1+9x+8x^2)}{x}$

The x in the numerator and the x in the denominator cancel

1+9x+8x^2

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Example Question #45 : Exponents

Solve:

$x^{6}\cdot x^{12}$

Possible Answers:

$x^{6}$

$x^{2}$

$x^{\frac{1}{2}}$

$x^{18}$

Correct answer:

$x^{18}$

Explanation:

When multiplying expressions with the same variable, combine terms by adding the exponents, while leaving the variable unchanged. For this problem, we do that by adding 6+12, to get a new exponent of 18:

$x^{6}\cdot x^{12}=x ^{6+12}=x^{18}$

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Example Question #46 : Exponents

Solve:

$x^{2}\cdot x$

Possible Answers:

$x^{2}$

$x^{5}$

$x^{3}$

Correct answer:

$x^{3}$

Explanation:

When multiplying expressions with the same variable, combine terms by adding the exponents, while leaving the variable unchanged. For this problem, we do that by adding 2+1, to get a new exponent of 3:

$x^{2}\cdot x=x ^{2+1}=x^{3}$

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SAT Math : Exponential Operations

Study concepts, example questions & explanations for SAT Math

All SAT Math Resources

Example Questions

Example Question #41 : Exponents

Example Question #41 : Exponents

Example Question #41 : How To Multiply Exponents

Example Question #44 : Exponents

Example Question #42 : Exponents

Example Question #43 : Exponents

Example Question #44 : Exponents

Example Question #48 : Exponents

Example Question #45 : Exponents

Example Question #46 : Exponents

All SAT Math Resources

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