Powers and roots

A short way to write repeated multiplication.

Doubling and doubling

1, 2, 4, 8, 16, 32 … doubling grows very fast. Square 10 has 2 × 2 × 2 × 2 × 2 × 2 × 2 × 2 × 2 = 512 grains. We need a short way to write repeated multiplication.

Powers

2³ is a power: 2 multiplied by itself 3 times. The small 3 is the exponent. 5² is “5 squared”; 2³ is “2 cubed”.

Square roots

36 dots make a 6 by 6 square. So the square root of 36 is 6: √36 = 6. Squaring and square roots undo each other: 6² = 36 and √36 = 6.

Powers of ten

10⁶ is a million; 10⁹ is a billion. Bangladesh has about 1.7 × 10⁸ people – 170 million. Scientists write huge numbers this way: the Sun is about 1.5 × 10⁸ km away.

What I learnt

I understand powers as repeated multiplication.
I know square roots undo squaring.
I can use powers of 10 for large numbers.