Powers are repeated multiplication
- 4² (four squared) = 4 × 4 = 16, not 4 × 2.
- 2⁵ = 2 × 2 × 2 × 2 × 2 = 32. The small number, the index, says how many times to multiply.
- √49 = 7 because 7² = 49. ∛64 = 4 because 4³ = 64. A negative number has a cube root: ∛(−8) = −2.
Learn the squares up to 15² = 225 and the cubes 1, 8, 27, 64, 125, and 1000 = 10³.
Negatives and brackets
(−3)² = (−3) × (−3) = 9, but −3² = −(3²) = −9: the power is done before the minus sign. A calculator gives the same: type (−3)² with the brackets.
In the order of operations, powers and roots come straight after brackets: 2 + 3² × 4 = 2 + 9 × 4 = 38.
To estimate √40: 6² = 36 and 7² = 49, and 40 is much nearer 36, so √40 is a little more than 6, about 6.3.
Powers on the calculator
Work out (−3)² and then −3² on the calculator, typing exactly what you see. Then work out (2.4³ + √150) ÷ 1.8², with brackets round the top, and round to 3 significant figures.