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

Answer:

Part A: 0

Part B: All real numbers

Step-by-step 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!