Use positive integer indices to write, for example, \(2×2×2×2=2^4\)

Use negative integer indices to represent reciprocals.

Use fractional indices to represent roots and combinations of powers and roots.

Calculate positive integer powers and exact roots.

e.g. \(2^4=16\)

\(\sqrt{9}=3\)

\(\sqrt[3]{8}=2\)

Recognise simple powers of 2, 3, 4 and 5.

e.g. \(27=3^3\)

[see also Inverse operations, 1.04a]

Calculate with integer powers.

e.g. \(2^{-3} = \dfrac{1}{8}\)

Calculate with roots.

Calculate fractional powers.

e.g. \(16^{\frac{-3}{4}} = \dfrac{1}{(\sqrt[4]{16})^3} = \dfrac{1}{8}\)

Estimate powers and roots.

e.g. \(\sqrt{51}\) to the nearest whole number

[see also Simplifying products and quoients, 6.01c]

Know and apply:

\(a^m × a^n = a^{m+n}\)

\(a^m ÷ a^n = a^{m-n}\)

\((a^m)^n = a^{mn}\)

[see also Calculations with numbers in standard form, 3.02b, Simplifying products and quotients, 6.01c]