Question

PLEASE HELP I HAVE 30 POINTS Part A: If (6^2)^x = 1, what is the value of x? Explain your answer. (5 points) Part B: If (6^0)^x = 1, what are the possible values of x? Explain your answer. (5 points)

Answer 1

Part A: 0

Part B: All real numbers

Explanation:

Part A:

We have:

`(6^2)^x=1`

First, let's evaluate the square:

`36^x=1`

Now, what to the xth power will equal 1?

Remember the fact that anything (except for 0) to the zeroth power is 1.

Therefore, our x is 0:

`36^0=1`

Part B:

We have:

`(6^0)^x=1`

Like mentioned previously, anything to the zeroth power is 1. Thus:

`1^x=1`

Now, 1 is a special base because 1 to any (real) power is still going to be 1. For example:

`1^0=1,1^1=1,1^(999),\text{ and } 1^(\pi)=1`

Therefore, our values of x is all real numbers.

And we're done!