Question

Part A: If (6^2)^x = 1, what is the value of x? Explain your answer.

Answer 1

Answer:

$\Large\boxed{PART\ A:\ x=0}\\\\\boxed{PART\ B:\ x\in\mathbb{R}}$

Step-by-step explanation:

$\text{We know:}\ a^0=1\ \text{for any real number except 0.}\\\\PART\ A:\\(6^2)^x=1\qquad\text{use}\ (a^n)^m=a^{nm}\\\\6^{2x}=1\iff2x=0\qquad\text{divide both sides by 2}\\\\\boxed{x=0}\\\\PART\ B:\\(6^0)^x=1\to1^x=1\\\\\text{We know}\ 1^a=1\ \text{for any value of a.}\ \text{Therefore}\ \boxed{x\in\mathbb{R}}$