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

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}`