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 times a times a times a times a )(a times a)`
= a x a x a
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.
1. Simplify a x a2.
a x a2 = a x a x a = a3
2. Simplify y7 ÷ y3
y7 ÷ y3 = y(7 - 3) = y4