Powers and index laws

What 2^5 really means, and the three laws that make big powers easy. About 8 minutes, GCSE.

What you will do

1. What a power means. 2^5 means five 2s multiplied together: 2 × 2 × 2 × 2 × 2 = 32. The small number is the power (or index); the big number is the base.
2. Multiplying powers of the same base. 3^2 × 3^4 means two 3s times four 3s - six 3s in all. So the powers add: 3^6.
3. A power of a power. (2^3)^2 means 2^3 multiplied by itself: six 2s. So the powers multiply.
4. Negative powers. A negative power does not make a negative number. It means "one over": 2^-3 = 1/2^3 = 1/8.
5. Careful with minus signs. (-3)^2 means (-3) × (-3) = 9. But -3^2 means the power happens first, then the minus: -9.