# A Guide to the GRE/Exponents

## Contents

# Exponents[edit]

The GRE frequently tests **exponents**, which are numbers indicating how many times a value has been multiplied into a given system.

### Rule[edit]

**When multiplying exponents, add the exponent numbers; when raising exponents to a power, multiply the exponent numbers.**

An exponent is a statement of how many times a number has been multiplied into a given system. 25 is equal to 5^{2} or 5(5). Multiplying 5^{2} by 5^{2} equals 5(5)(5)(5) or 5^{4}. Raising an exponent to a power multiplies the exponent numbers, while multiplying exponents merely adds their numbers.

*a*^{3}(*a*^{4}) =*a*^{7}

- (
*b*^{5})^{6}=*b*^{30}

A negative exponent equals one divided by the number raised to that exponent; a fractional exponent indicates a radical of the corresponding degree.

#### Exponent of "0" is equal to 1[edit]

A number with an exponent of “0” equals 1.

*x*^{0} = 1

### Practice[edit]

1. What does *y*^{2}(*y*^{5}) equal?

2. If (*m*^{4})^{4} = *m*^{x} what does *x* equal?

3. If is equal to *q*^{-2} then what does *q* equal?

### Answers to Practice Questions[edit]

1. *y*^{7}

When multiplying, add the exponent numbers.

2. 16

When raising exponents to a power, multiply the exponent numbers.

3.

Negative exponents indicate 1 divided by the number raised to this exponent.

*q*^{-2} is so since *q*^{-2} = , then *q*^{2} must equal 2 and *q* must equal .