GRE Math : How to divide exponents

Example Questions

Example Question #1 : Exponential Operations

Simplify

None

Explanation:

Divide the coefficients and subtract the exponents.

Example Question #32 : Exponents

Which of the following is equal to the expression , where

xyz ≠ 0?

z/(xy)

xyz

1/y

xy

z

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 #2 : Exponential Operations

If , then

Cannot be determined

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 #3 : How To Divide Exponents

If , which of the following is equal to ?

a6

a

a18

a4

The answer cannot be determined from the above information

a18

Explanation:

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

Example Question #444 : Algebra

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

30

–5

9

–30

16

–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 : Exponential Operations

Evaluate:

Explanation:

Distribute the outside exponents first:

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