Question

State the power law of exponents.

Answer 1

The "power rule" tell us that to raise a power to a power, just multiply the exponents. 

If a is any real number and m, n are positive integers, then  `(a^m)^n = a^(mn)`

We have,

`(a^m)^n = a^m xx a^m xx a^m xx ....n  ` factors

`(a^m)^n  = (a xx a xx a xx... m ) xx (a xx a xx a xx... m ).... n `factors

`(a^m)^n =(a xx a xx a xx... m )`

Hence, `(a^m)^n = a^(mn)`