Year 10: Integer indices

This cheat sheet covers integer indices, a key concept in Algebra. Understanding this topic will help you with many future mathematical concepts.

What are integer indices?

Integer indices are a shorthand way of writing repeated multiplication. They represent a number raised to a power.

$x^{n} = x \times x$ * ... * x (n times)
$x^{m} \times x^{n} = x^{m + n}$ (When multiplying, add the indices)
$x^{m} / x^{n} = x^{m - n}$ (When dividing, subtract the indices)
${(x^{m})}^{n} = x^{m \times n}$ (When raising to a power, multiply the indices)
$x^{0} = 1$ (Any number (except 0) raised to the power of 0 is equal to 1)
0⁰ does not have an agreed-upon value

Example 1: $2^{3} = 2 \times 2 \times 2 = 8$

Example 2: $3^{2} \times 4^{2} = 9 \times 16 = 144$

Example 3: $5^{4} / 5^{2} = 625 / 25 = 25$