GRE Math : How to divide exponents

Study concepts, example questions & explanations for GRE Math

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Example Questions

Example Question #124 : Exponential Operations

Simplify

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

Possible Answers:

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

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

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

Example Question #2 : How To Divide Exponents

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

xyz ≠ 0?

Possible Answers:

xy

z

z/(xy)

1/y

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. 

Example Question #126 : Exponential Operations

If , then

 

Possible Answers:

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.

 

Example Question #1 : How To Divide Exponents

If , which of the following is equal to ?

Possible Answers:

a6

a4

a18

a

The answer cannot be determined from the above information

Correct answer:

a18

Explanation:

The numerator is simplified to  (by adding the exponents), then cube the result. a24/a6 can then be simplified to .

Example Question #1 : How To Divide Exponents

[641/2 + (–8)1/3] * [43/16 – 3171/3169] = 

Possible Answers:

–5

9

–30

16

30

Correct answer:

–30

Explanation:

Let's look at the two parts of the multiplication separately. Remember that (–8)1/3 will be negative. Then 641/2 + (–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 = 3171–169 = 32 = 9. So 43/16 – 3171/3169 = 4 – 9 = –5. 

Together, [641/2 + (–8)1/3] * [43/16 – 3171/3169] = 6 * (–5) = –30.

Example Question #1 : How To Divide Exponents

Evaluate:

 

Possible Answers:

 

 

 

Correct answer:

Explanation:

Distribute the outside exponents first:

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

 

 

Example Question #3 : How To Divide Exponents

Possible Answers:

\dpi{100} \small 7

\dpi{100} \small 343

\dpi{100} \small 42

\dpi{100} \small 28

\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 

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

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