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PSAT Math : How to divide exponents

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Example Questions

Example Question #6 : How To Divide Exponents

5⁴/ 25 =

Possible Answers:

5⁴ / 5

Correct answer:

Explanation:

25 = 5 * 5 = 5². Then 5⁴ / 25 = 5⁴ / 5².

Now we can subtract the exponents because the operation is division. 5⁴ / 5²= 5^{4 – 2} = 5² = 25. The answer is therefore 25.

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Example Question #121 : Exponential Operations

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

Possible Answers:

$605^{4}$

$5^2\cdot11^6$

11^6

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

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

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 #2 : How To Divide Exponents

Simplify

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

Possible Answers:

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

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

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

None

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

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 #3 : How To Divide Exponents

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

xyz ≠ 0?

Possible Answers:

1/y

z/(xy)

xyz

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 #4 : 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 #11 : 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:

a⁴

a¹⁸

The answer cannot be determined from the above information

a⁶

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 #2 : Exponential Operations

$\dpi{100} \small \frac{7^{10}-7^{8}}{7^{9}-7^{7}}=$

Possible Answers:

$\dpi{100} \small 28$

$\dpi{100} \small 49$

$\dpi{100} \small 343$

$\dpi{100} \small 42$

$\dpi{100} \small 7$

Correct answer:

$\dpi{100} \small 7$

Explanation:

The easiest way to solve this is to simplify the fraction as much as possible. We can do this by factoring out the greatest common factor of the numerator and the denominator. In this case, the GCF is 7^7 .

$\frac{7^7\left ( 7^3-7^1\right)}{7^7\left ( 7^2-1\right)}$

Now, we can cancel out the 7^7 from the numerator and denominator and continue simplifying the expression.

$\frac{7^7\left ( 7^3-7^1\right)}{7^7\left ( 7^2-1\right)}=\frac{7^3-7^1}{7^2-1}=\frac{343-7}{49-1}=\frac{336}{48}=7$

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PSAT Math : How to divide exponents

Study concepts, example questions & explanations for PSAT Math

All PSAT Math Resources

Example Questions

Example Question #6 : How To Divide Exponents

Example Question #121 : Exponential Operations

Example Question #2 : How To Divide Exponents

Example Question #3 : How To Divide Exponents

Example Question #4 : How To Divide Exponents

Example Question #11 : How To Divide Exponents

Example Question #2 : Exponential Operations

All PSAT Math Resources

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