# What does it mean a number to the 5th or 6th power mean?

May 22, 2018

It means that the number is multiplied by itself that many times.

#### Explanation:

As I said in the answer, we can think of exponents as a way of shortening the statement "A number $n$ multiplied by itself $i$ times"

If we wrote the quoted statement as a mathematical expression:

$n \times n \times n \times n \ldots \times n = {n}^{i}$

Translating this abstract explanation into a more concrete example:

${2}^{1} = 2$

${2}^{2} = 2 \times 2$

${2}^{3} = 2 \times 2 \times 2$

${2}^{4} = 2 \times 2 \times 2 \times 2$

${2}^{5} = 2 \times 2 \times 2 \times 2 \times 2$

The special conditions here are fractional/decimal exponents and zero.

A number raised to a fraction is the same as saying the "$k$th root" of a number raised to the $i$th power:

${n}^{\frac{i}{k}} = \sqrt[k]{{n}^{i}}$

An exponent of zero always results in 1:

${1}^{0} = 1$

${2}^{0} = 1$

...

${750}^{0} = 1$

${n}^{0} = 1$