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 = m^x what does x equal?

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

Answers to Practice Questions

1. y⁷

When multiplying, add the exponent numbers.

2. 16

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

3. ${\sqrt {2}}$

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

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