college algebra word problem

Question

In the formula A = πr², if r is tripled, what is the effect on A?

Answer 1

A1=pir^2

A2 = pi(r^3)^2 = pi(r^2)^3 = A1^3

The new area is the old area cubed

(r^3)^2 = r^6 = (r^2)^3

for example

(2^2)^3 = 4^3 = 64 = (2^3)^2 = 8^2 = 64

the exponents multiply (a^n)^m = a^nm = (a^m)^n

so you can interchange them, similar to ab = ba