Question

Why does the rule to multiply the exponents when raising a power to a power work the way it does? In other words, why does (2^3)^4=2^12?

Answer 1

2^3 = 2*2*2
(2^3) ^4 means (2*2*2)(2*2*2)(2*2*2)(2*2*2) = 2^12

Answer 2

(2^3)^4 = 2^(3*4)=2^12