### All GRE Math Resources

## Example Questions

### Example Question #1 : Exponential Operations

Simplify

**Possible Answers:**

None

**Correct answer:**

Divide the coefficients and subtract the exponents.

### Example Question #2 : Exponential Operations

Which of the following is equal to the expression , where

xyz ≠ 0?

**Possible Answers:**

1/y

xy

z/(xy)

z

xyz

**Correct answer:**

1/y

(xy)^{4} can be rewritten as x^{4}y^{4} and z^{0} = 1 because a number to the zero power equals 1. After simplifying, you get 1/y.

### Example Question #3 : Exponential Operations

If , then

**Possible Answers:**

Cannot be determined

**Correct answer:**

Start by simplifying the numerator and denominator separately. In the numerator, (c^{3})^{2} is equal to c^{6}. In the denominator, c^{2 }* c^{4} equals c^{6} as well. Dividing the numerator by the denominator, c^{6}/c^{6}, gives an answer of 1, because the numerator and the denominator are the equivalent.

### Example Question #4 : Exponential Operations

If , which of the following is equal to ?

**Possible Answers:**

a^{18}

The answer cannot be determined from the above information

a^{4}

a^{6}

a

**Correct answer:**

a^{18}

The numerator is simplified to (by adding the exponents), then cube the result. a^{24}/a^{6} can then be simplified to .

### Example Question #1 : Exponential Operations

[64^{1/2} + (–8)^{1/3}] * [4^{3}/16 – 3^{171}/3^{169}] =

**Possible Answers:**

30

9

–5

–30

16

**Correct answer:**

–30

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. 4^{3}/16 = 4^{3}/4^{2} = 4. Similarly, 3^{171}/3^{169} = 3^{171–169} = 3^{2} = 9. So 4^{3}/16 – 3^{171}/3^{169 }= 4 – 9 = –5.

Together, [64^{1/2} + (–8)^{1/3}] * [4^{3}/16 – 3^{171}/3^{169}] = 6 * (–5) = –30.

### Example Question #5 : Exponential Operations

Evaluate:

**Possible Answers:**

**Correct answer:**

Distribute the outside exponents first:

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

### Example Question #6 : Exponential Operations

**Possible Answers:**

**Correct answer:**

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.