Powers & Roots
Year 8 🔢 Number Squares, cubes, square roots, cube roots and index notation.
² Powers (Indices)
A power (or index) tells you how many times to multiply a number by itself.
Definition
$$a^n = \underbrace{a \times a \times a \cdots a}_{n \text{ times}}$$Examples: $2^3 = 8$, $5^2 = 25$, $3^4 = 81$, $10^6 = 1{,}000{,}000$
√ Square & Cube Roots
The square root undoes squaring. The cube root undoes cubing.
Roots
$$\sqrt{a^2} = a \qquad \sqrt[3]{a^3} = a$$Examples: $\sqrt{49} = 7$, $\sqrt{144} = 12$, $\sqrt[3]{27} = 3$
📏 Laws of Indices
Laws of Indices
$$a^m \times a^n = a^{m+n} \qquad a^m \div a^n = a^{m-n} \qquad (a^m)^n = a^{mn}$$
$$a^0 = 1 \qquad a^{-n} = \frac{1}{a^n} \qquad a^{\frac{1}{2}} = \sqrt{a}$$
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