Question

Without using the exponent law (x^a)^b = x^ab, show that (8^-2)^3 = 1/8^6.

Answer 1

It is required to prove:

`(8^(-2))^3=(1)/(8^6)`

To prove without using the exponent law (x^a)^b = x^ab

So, find the value of each side

so,

The left side =

`(8^(-2))^3=((1)/(8^2))^3=((1)/(64))^3=(1^3)/(64^3)=(1)/(64\cdot64\cdot64)=(1)/(262,144)`

The right side =

`(1)/(8^6)=(1)/(8\cdot8\cdot8\cdot8\cdot8\cdot8)=(1)/(262,144)`

so, the left side = the right side