Question

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

Part B: If (6^0)^x = 1, what are the possible values of x? Explain your answer.

Answer 1

Step-by-step explanation:

A.

$(6^2)^x=1\\\\36^x=1\\\\36^x=36^0\Rightarrow x=0$

Every number to the power of 0 gives us 1

$a^0=1\ \text{for}\ a\in\mathbb{R}$

B.

$(6^0)^x=1\\\\1^x=1\\\\x\in\mathbb{R}$

1 to the any power gives us 1.

$1^n=1\ \text{for}\ n\in\mathbb{R}$