# Exponents

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

## Rule

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 52 or 5(5). Multiplying 52 by 52 equals 5(5)(5)(5) or 54. Raising an exponent to a power multiplies the exponent numbers, while multiplying exponents merely adds their numbers.

a3(a4) = a7
(b5)6 = b30

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

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

x0 = 1

## Practice

1. What does y2(y5) equal?

2. If (m4)4 = mx what does x equal?

3. If ${\displaystyle {\tfrac {1}{2}}}$ is equal to q−2 then what does q equal?

1. y7

When multiplying, add the exponent numbers.

2. 16

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

3. ${\displaystyle {\sqrt {2}}}$

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

q−2 is ${\displaystyle {\tfrac {1}{q^{2}}}}$ so since q−2 = ${\displaystyle {\tfrac {1}{2}}}$, then q2 must equal 2 and q must equal ${\displaystyle {\sqrt {2}}}$.