Question

Show that a^12 can be written as a perfect square and a perfect cube

Answer 1

Explanation:

Doing this the long way, write a^12 as a product of "a"s

a^12 = a * a * a * a * a * a * a * a * a * a * a * a

Now group them into groups of 4

a^12 = a * a * a * a * a * a * a * a * a * a * a * a

There are 3 groups of 4 so you can write it as [(a^4)]^3 which is a cube

Now do the same thing with groups of 6s

a^12 = a * a * a * a * a * a * a * a * a * a * a * a

a^12 = (a^6)^2

So the two answers are

Perfect cube: [(a^4)]^3

Perfect square: (a^6)^2