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SAT Math : How to divide exponents

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Example Questions

Example Question #31 : How To Divide Exponents

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

Possible Answers:

4^6

2^9

$8^{-7}$

$2^{-7}$

2^8

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 #32 : How To Divide Exponents

Solve:

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

Possible Answers:

$x^{12}$

$x^{4}$

$x^{3}$

$x^{8}$

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 #33 : How To Divide Exponents

Solve:

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

Possible Answers:

$x^{2}$

$x^{18}$

$x^{6}$

$x^{3}$

Correct answer:

$x^{6}$

Explanation:

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

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Example Question #34 : How To Divide Exponents

Solve:

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

Possible Answers:

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

$x^{9}$

$x^{5}$

Correct answer:

$x^{5}$

Explanation:

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

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Example Question #35 : How To Divide Exponents

Solve:

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

Possible Answers:

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

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

$x^{19}$

$x^{3}$

Correct answer:

$x^{3}$

Explanation:

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

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Example Question #36 : How To Divide 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 #37 : How To Divide Exponents

Solve:

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

Possible Answers:

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

$x^{6}$

$x^{3}$

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

Correct answer:

$x^{6}$

Explanation:

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

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Example Question #38 : How To Divide Exponents

Solve:

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

Possible Answers:

$x^{2}$

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

$\frac{1}{x}$

Correct answer:

Explanation:

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

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Example Question #39 : How To Divide Exponents

Solve:

$\frac{x^{\frac{3}{4}}}{x^{\frac{1}{4}}}$

Possible Answers:

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

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

$x^{2}$

$\frac{1}{x}$

Correct answer:

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

Explanation:

$\frac{x^{\frac{3}{4}}}{x^{\frac{1}{4}}}=x ^{\frac{3}{4}-\frac{1}{4}}=x^{\frac{2}{4}}=x^{\frac{1}{2}}$

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Example Question #40 : How To Divide Exponents

Solve:

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

Possible Answers:

$x^{\frac{1}{5}}$

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

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

Correct answer:

$x^{\frac{1}{5}}$

Explanation:

$\frac{x^{\frac{3}{5}}}{x^{\frac{2}{5}}}=x ^{\frac{3}{5}-\frac{2}{5}}=x^{\frac{1}{5}}$

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SAT Math : How to divide exponents

Study concepts, example questions & explanations for SAT Math

All SAT Math Resources

Example Questions

Example Question #31 : How To Divide Exponents

Example Question #32 : How To Divide Exponents

Example Question #33 : How To Divide Exponents

Example Question #34 : How To Divide Exponents

Example Question #35 : How To Divide Exponents

Example Question #36 : How To Divide Exponents

Example Question #37 : How To Divide Exponents

Example Question #38 : How To Divide Exponents

Example Question #39 : How To Divide Exponents

Example Question #40 : How To Divide Exponents

All SAT Math Resources

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