Terms with Powers

Terms with Powers

GCSE(F), GCSE(H),

As with numeric powers, a x a = a2, with the small 2 meaning that a has been multiplied by itself.

Multiplying a2 by a is the same as a x a x a, which is written as a3.

Multiplying the same letter with different powers is carried out by adding the powers:

a3 x a4 = a(3 + 4) = a7.

Dividing powers is similar, with the indices being subtracted.

a5 ÷ a2

= `frac(a^5)(a^2)`

= `frac(a times a times a times a times a )(a times a)`

= a x a x a

= a3

Therefore a5 ÷ a2 = a(5 - 3) = a3.

Additional and Higher: Make sure that the correct letters carry the correct power sign:

c3d x c2 = c(3 + 2)d = c5d.

Examples

1. Simplify a x a2.

Answer: a3

a x a2 = a x a x a = a3

2. Simplify y7 ÷ y3

Answer: y4

y7 ÷ y3 = y(7 - 3) = y4