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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.
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.