Year 9: Integer indices

This cheat sheet covers integer indices - powers with negative and fractional exponents.

Key concepts

• Integer index: A number raised to a power, like xⁿ.
• Positive integer exponent:$x^n=x\times x$ * ... * x (n times)
• Negative integer exponent:$x^{-n}=1/x^n$ (Inverse of xⁿ)
• Fractional Index:$x^{1/n}{=}^n$√x (nth root of x)

Rules

• $x^m\times x^n=x^{m+n}$ (Multiplying with the same base)
• $x^m/x^n=x^{m-n}$ (Dividing with the same base)
• ${\left(x^m\right)}^n=x^{m\times n}$ (Raising a power to another power)
• ${(x^m\times y^n)}^m=x^{m\times n}\times y^{m\times n}$ (Order of operations - BIDMAS/BODMAS)

Examples

Example 1:$2^{-3}=1/2^3=1/8$

Example 2:$3^2=3\times 3=9$

Example 3:$4^{1/2}{=}^2$√$4=2$

Remember to simplify your answers as much as possible!