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SAT Math : Exponential Operations

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Example Questions

Example Question #21 : How To Divide Exponents

Evaluate $7^{90}\div7^{16}$

Possible Answers:

$7^{25}$

7^5

$7^{35}$

$7^{74}$

$7^{18}$

Correct answer:

$7^{74}$

Explanation:

When dividing exponents with the same base, we just subtract the exponents and keep the base the same.

$7^{90}\div7^{16}=7^{90-16}=7^{74}$

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Example Question #22 : How To Divide Exponents

Evaluate $9^8\div9^{-3}$

Possible Answers:

9^5

$9^{-24}$

$9^{-12}$

$9^{11}$

9^6

Correct answer:

$9^{11}$

Explanation:

When dividing exponents with the same base, we just subtract the exponents and keep the base the same.

$9^8\div9^{-3}=9^{8-(-3)}=9^{11}$

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Example Question #141 : Exponents

Evaluate $16^5\div2^{12}$

Possible Answers:

$2^{-7}$

2^9

4^6

2^8

$8^{-7}$

Correct answer:

2^8

Explanation:

Although we have different bases, we know that 16=2^4 . Therefore we know that $(2^4)^5\div2^{12}=2^{20-12}=2^8$

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Example Question #142 : Exponents

Solve:

$\frac{x^{6}}{x^{2}}$

Possible Answers:

$x^{3}$

$x^{8}$

$x^{4}$

$x^{12}$

Correct answer:

$x^{4}$

Explanation:

When dividing expressions with the same variable, combine terms by subtracting the exponents, while leaving the variable unchanged. For this problem, we do that by subtracting 6-2, to get a new exponent of 4:

$\frac{x^{6}}{x^{2}}=x ^{6-2}=x^{4}$

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Example Question #143 : Exponents

Solve:

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

Possible Answers:

$x^{18}$

$x^{3}$

$x^{2}$

$x^{6}$

Correct answer:

$x^{6}$

Explanation:

$\frac{x^{12}}{x^{6}}=x ^{12-6}=x^{6}$

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Example Question #144 : Exponents

Solve:

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

Possible Answers:

$x^{5}$

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

$x^{9}$

Correct answer:

$x^{5}$

Explanation:

$\frac{x^{7}}{x^{2}}=x ^{7-2}=x^{5}$

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Example Question #145 : Exponents

Solve:

$\frac{x^{11}}{x^{8}}$

Possible Answers:

$x^{19}$

$\frac{1}{x^{3}}$

$x^{\frac{11}{8}}$

$x^{3}$

Correct answer:

$x^{3}$

Explanation:

$\frac{x^{11}}{x^{8}}=x ^{11-8}=x^{3}$

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Example Question #146 : Exponents

Solve:

$\frac{x^{18}}{x^{17}}$

Possible Answers:

$x^{\frac{18}{17}}$

$x^{25}$

$\frac{1}{x}$

Correct answer:

Explanation:

$\frac{x^{18}}{x^{17}}=x ^{18-17}=x^{1}=x$

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Example Question #141 : Exponential Operations

Solve:

$\frac{x^{9}}{x^{3}}$

Possible Answers:

$\frac{1}{x^{6}}$

$x^{3}$

$x^{6}$

$\frac{1}{x^{3}}$

Correct answer:

$x^{6}$

Explanation:

$\frac{x^{9}}{x^{3}}=x ^{9-3}=x^{6}$

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Example Question #148 : Exponents

Solve:

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

Possible Answers:

$\frac{1}{x}$

$x^{2}$

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

Correct answer:

Explanation:

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

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SAT Math : Exponential Operations

Study concepts, example questions & explanations for SAT Math

All SAT Math Resources

Example Questions

Example Question #21 : How To Divide Exponents

Example Question #22 : How To Divide Exponents

Example Question #141 : Exponents

Example Question #142 : Exponents

Example Question #143 : Exponents

Example Question #144 : Exponents

Example Question #145 : Exponents

Example Question #146 : Exponents

Example Question #141 : Exponential Operations

Example Question #148 : Exponents

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