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# Introduction to indices

Indices are used when you multiply a number by itself several times.

They make the multiplication easier to read and write.

$$\Tblue{3} \times \Tblue{3} \times \Tblue{3} \times \Tblue{3} = \Tblue{3}^\Tred{4} = 81,\quad \Tblue{-2} \times \Tblue{-2} = (\Tblue{-2})^\Tred{2} = 4$$

The number being multiplied is the base ($\Tblue{3}$). The base is raised to the power of the index ($\Tred{4}$).

This process is called exponentiation.

A power of two is a square. A power of three is a cube.

Twelve square: $12 \times 12 = 12^2 = 144$

Four cubed: $4 \times 4 \times 4 = 4^3 = 64$.

Any number except for 0 raised to the power 0 is 1. A number raised to the power of 1 is itself.

$$2^\Tred{0} = 1,\quad 2^\Tred{1} = 2,\quad 2^\Tred{2} = 2\times2 = 4,\quad 2^\Tred{3} = 2\times 2\times 2 = 8.$$
The area of a square $A$ is equal to the length $a$ of its sides squared. The volume of a cube $V$ is equal to the length $a$ of its sides cubed.