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SAT Math : How to divide exponents

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Example Questions

Example Question #31 : Exponents

$\frac{55^{10}}{121^6} \cdot \frac{11^8}{5^{8}} = ?$

Possible Answers:

$605^{4}$

$\frac{5^2}{11^4}$

$\frac{5^{18}}{11^4}$

11^6

$5^2\cdot11^6$

Correct answer:

$5^2\cdot11^6$

Explanation:

The key to this problem is understanding how exponents divide. When two exponents have the same base, then the exponent on the bottom can simply be subtracted from the exponent on top. I.e.:

$\frac{5^x}{5^y} = 5^{x-y}$

Keeping this in mind, we simply break the problem down into prime factors, multiply out the exponents, and solve.

$\frac{55^{10}}{121^6} \cdot \frac{11^8}{5^8} = \frac{(5\cdot 11)^{10}}{5^8}\cdot \frac{11^8}{(11\cdot11)^6} = 11^{10}\cdot\frac{5^{10}}{5^8} \cdot \frac{11^8}{11^{12}} = 5^2 \cdot \frac{11^{10+8}}{11^{12}} = 5^2\cdot11^6$

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Example Question #4 : How To Divide Exponents

Simplify

$\dpi{100} \small \frac{20x^{4}y^{-3}z^{2}}{5z^{-1}y^{2}x^{2}}=$

Possible Answers:

$\dpi{100} \small \frac{4x^{2}z^{3}}{y^{5}}$

None

$\dpi{100} \small 15x^{-2}y^{-2}z^{-2}$

$\dpi{100} \small {4x^{5}y^{-2}}$

$\dpi{100} \small 15x^{2}y^{2}z^{2}$

Correct answer:

$\dpi{100} \small \frac{4x^{2}z^{3}}{y^{5}}$

Explanation:

Divide the coefficients and subtract the exponents.

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Example Question #5 : How To Divide Exponents

Which of the following is equal to the expression Equationgre , where

xyz ≠ 0?

Possible Answers:

xyz

z/(xy)

1/y

Correct answer:

1/y

Explanation:

(xy)⁴ can be rewritten as x⁴y⁴ and z⁰ = 1 because a number to the zero power equals 1. After simplifying, you get 1/y.

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Example Question #11 : How To Divide Exponents

If $c\neq 0$ , then $\frac{(c^3)^2}{c^2c^4}=?$

Possible Answers:

c^4

Cannot be determined

c^2

Correct answer:

Explanation:

Start by simplifying the numerator and denominator separately. In the numerator, (c³)² is equal to c⁶. In the denominator, c²* c⁴ equals c⁶ as well. Dividing the numerator by the denominator, c⁶/c⁶, gives an answer of 1, because the numerator and the denominator are the equivalent.

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Example Question #2 : How To Divide Exponents

If $a\not\equiv0$ , which of the following is equal to $\frac{(a^6*a^2)^3}{a^6}$ ?

Possible Answers:

The answer cannot be determined from the above information

a⁴

a⁶

a¹⁸

Correct answer:

a¹⁸

Explanation:

The numerator is simplified to a^8 (by adding the exponents), then cube the result. a²⁴/a⁶ can then be simplified to $a^{18}$ .

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Example Question #11 : How To Divide Exponents

$\frac{2^9}{2^6}$

Possible Answers:

$2^{1.5}$

2^9-3

2^3

$2^{15}$

$2^{54}$

Correct answer:

2^3

Explanation:

When dividing exponents, we need to make sure we have the same base. In this case we do. Then we just subtract the exponents. The answer is $2^{9-6}=2^3$ .

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Example Question #12 : How To Divide Exponents

$\frac{3^{57}}{3^{19}}$

Possible Answers:

3^3

$3^{24}$

$3^{38}$

$3^{76}$

$3^{1083}$

Correct answer:

$3^{38}$

Explanation:

When dividing exponents, we need to make sure we have the same base. In this case we do. Then we just subtract the exponents. The answer is $3^{57-19}=3^{38}$ .

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Example Question #13 : How To Divide Exponents

$\frac{9^7}{7^9}$

Possible Answers:

$9^{-2}$

$7^{-2}$

None of the possible answers

7^2

9^2

Correct answer:

None of the possible answers

Explanation:

When dividing exponents, we need to make sure we have the same base. In this case we don't. We can't really simplify it and we can't subtract with different bases so the answer is none of the possible answers.

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Example Question #14 : How To Divide Exponents

$\frac{10^{12}}{10^{10}}$

Possible Answers:

$10^{120}$

$10^{1200}$

1000

$10^{22}$

100

Correct answer:

100

Explanation:

When dividing exponents, we need to make sure we have the same base. In this case we do. Then we just subtract the exponents. The answer is $10^{12-10}=10^2$ . 10^2 is just 10*10 or 100 .

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Example Question #541 : Algebra

$\frac{4^7}{4^-8}$

Possible Answers:

$4^{-15}$

$4^{-1}$

$4^{56}$

$4^{-56}$

$4^{15}$

Correct answer:

$4^{15}$

Explanation:

When dividing exponents, we need to make sure we have the same base. In this case we do. Then we just subtract the exponents. Since we arre subtracting wit a negative alue, this becomes an addition problem. The answer is $4^{7-(-8)}=4^{7+8}=4^{15}$ .

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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 : Exponents

Example Question #4 : How To Divide Exponents

Example Question #5 : How To Divide Exponents

Example Question #11 : How To Divide Exponents

Example Question #2 : How To Divide Exponents

Example Question #11 : How To Divide Exponents

Example Question #12 : How To Divide Exponents

Example Question #13 : How To Divide Exponents

Example Question #14 : How To Divide Exponents

Example Question #541 : Algebra

All SAT Math Resources

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