Year 10: Integer indices

This cheat-sheet covers integer indices in Year 10 Algebra.

Key concepts

What is an Integer index? An integer index (also known as a power) indicates how many times a base is multiplied by itself. For example, x³ means $x \times x \times x$ .
$x^{0} = 1$ Any non-zero number raised to the power of 0 is equal to 1.
$x^{- n} = 1 / x^{n}$ A negative integer index means taking the reciprocal of the base raised to the positive integer index.
$x^{- n} = 1$ ÷ xⁿ For example, $2^{- 3} = 1$ ÷ $2^{3} = 1$ ÷ $8 = 0.125$

${(x^{m})}^{n} = x^{m \times n}$ Raise the entire power to another power.
$x^{m} \times x^{n} = x^{m + n}$ Add the integer indices when multiplying terms with the same base.
$x^{m} / x^{n} = x^{m - n}$ Subtract the integer indices when dividing terms with the same base.

Example 1: $2^{4} \times 2^{2} = 2^{6} = 64$

Example 2: $5^{3} / 5^{1} = 5^{2} = 25$