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What Are Powers?

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

Powers

A power is an expression

a^{b} = \underset{b times}{\underset{⏟}{a \cdot a \cdot a \cdot . . . a}}

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

Power

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

\begin{array}{l} 5^{0} = 1 \\ 10 0^{0} = 1 \end{array}

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Activities 1