A power consists of a base and an exponent. Powers are used to write multiplication in an easier, more accessible way, and to simplify calculations. If you multiply a number by itself multiple times, it can be written as a power.

Theory

A power is an expression

$${a}^{b}=\underset{\text{}b\text{times}}{\underbrace{\phantom{\rule{3.0pt}{0ex}}a\cdot a\cdot a\cdot \phantom{\rule{3.0pt}{0ex}}...\phantom{\rule{3.0pt}{0ex}}a\phantom{\rule{3.0pt}{0ex}}}}$$ |

where $a$ is called the base, and $b$ is the exponent.

The base $a$ is the number that you multiply by itself, and $b$ is how many times you will be multiplying $a$ by itself.

Example 1

**Write 3 multiplied by itself 4 times as a power **

$$3\times 3\times 3\times 3={3}^{4}$$ |

Example 2

**Write the number 25 as a power with 5 as a base **

$$25=5\times 5={5}^{2}$$ |

**Note!** If the exponent is equal to 0, the value of the power is always 1, for all bases apart from 0.

Example 3

** **

Calculate ${5}^{0}$ and $10{0}^{0}$

$$\begin{array}{lll}\hfill {5}^{0}=1& \phantom{\rule{2em}{0ex}}& \hfill \\ \hfill 10{0}^{0}=1& \phantom{\rule{2em}{0ex}}& \hfill \end{array}$$

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