Question

Consider the equation (x^m)=(x^13)^5 x(x^-8)^-5

The value of m is

A. 15

B. 28

C. 35

D. 70

Answer 1

m = 106

Explanation:

`x^m=(x^(13))^5x(x^(-8))^(-5)\qquad\text{use}\ (a^n)^m=a^(nm)\\\\x^m=(x^((13)(5)))x(x^((-8)(-5)))\\\\x^m=(x^(65))x^1(x^(40))\qquad\text{use} \ a^na^m=a^(n+m)\\\\x^m=x^(65+1+40)\\\\x^m=x^(106)\Rightarrow m=106`