## Example Questions

### Example Question #1 : How To Divide Exponents

Simplify     None Explanation:

Divide the coefficients and subtract the exponents.

### Example Question #2 : How To Divide Exponents

Which of the following is equal to the expression , where

xyz ≠ 0?

xyz

z/(xy)

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 #1 : How To Divide Exponents

If , which of the following is equal to ?

a

The answer cannot be determined from the above information

a6

a4

a18

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] =

–30

16

9

–5

30

–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: ### Example Question #471 : Algebra       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. ### All GRE Math Resources 