GRE Math : How to divide exponents

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Example Question #1 : How To Divide Exponents

Simplify

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

Possible Answers:

None

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

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

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

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

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 #1 : How To Divide Exponents

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

xyz ≠ 0?

Possible Answers:

1/y

xyz

z/(xy)

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 #1 : How To Divide Exponents

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

Possible Answers:

c^4

c^2

Cannot be determined

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 #1 : 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:

a⁶

The answer cannot be determined from the above information

a⁴

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 #1 : How To Divide Exponents

[64^1/2 + (–8)^1/3] * [4³/16 – 3¹⁷¹/3¹⁶⁹] =

Possible Answers:

–30

–5

Correct answer:

–30

Explanation:

Let's look at the two parts of the multiplication separately. Remember that (–8)^1/3 will be negative. Then 64^1/2 + (–8)^1/3= 8 – 2 = 6.

For the second part, we can cancel some exponents to make this much easier. 4³/16 = 4³/4² = 4. Similarly, 3¹⁷¹/3¹⁶⁹ = 3^171–169 = 3² = 9. So 4³/16 – 3¹⁷¹/3¹⁶⁹= 4 – 9 = –5.

Together, [64^1/2 + (–8)^1/3] * [4³/16 – 3¹⁷¹/3¹⁶⁹] = 6 * (–5) = –30.

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Example Question #1 : Exponential Operations

Evaluate:

$\frac{(2x^3y^{-2}a^6z^4)^5}{(4xy^4a^{-3}z^4)^2}$

Possible Answers:

$\frac{2x^{13}a^{36}z^{12}}{y^{18}}$

$\frac{5x^{13}y-2az^{12}}{4}$

$\frac{5x^{13}y-2az^{12}}{4y}$

$2x^{13}-18a-36z^{12}$

$\frac{2x^{13}z^{12}}{y^{18}a^{36}}$

Correct answer:

$\frac{2x^{13}a^{36}z^{12}}{y^{18}}$

Explanation:

Distribute the outside exponents first:

$\frac{2^5x^{15}y^{-10}a^{30}z^{20}}{4^2x^2y^8a^{-6}z^8}$

Divide the coefficient by subtracting the denominator exponents from the corresponding numerator exponents:

$\frac{2x^{13}a^{36}z^{12}}{y^{18}}$

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Example Question #151 : Exponents

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

Possible Answers:

$\dpi{100} \small 28$

$\dpi{100} \small 42$

$\dpi{100} \small 7$

$\dpi{100} \small 343$

$\dpi{100} \small 49$

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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GRE Math : How to divide exponents

Study concepts, example questions & explanations for GRE Math

All GRE Math Resources

Example Questions

Example Question #1 : How To Divide Exponents

Example Question #1 : How To Divide Exponents

Example Question #1 : How To Divide Exponents

Example Question #1 : How To Divide Exponents

Example Question #1 : How To Divide Exponents

Example Question #1 : Exponential Operations

Example Question #151 : Exponents

All GRE Math Resources

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