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

(6^2)^x = 1
36^x = 1
x = 0 because 36^0 = 1

Answer 2

What is the answer for the second one?

Answer 3

What is 6^0 equal to?

Answer 4

1?

Answer 5

so its a 0 to?

Answer 6

(6^0)^x = 1
(1)^x = 1
The right hand side is 1 which can be written either as 1^0 or as 1^1 both of which are 1.
1^x = 1^0 implies x = 0
or
1^x = 1^1 implies x = 1

x = 0 or 1.

Answer 7

So 0 or 1 would work?

Answer 8

Hmm...

\(1^2=1\cdot1=1\\~\\1^3=1\cdot1\cdot1=1\\~\\1^4=1\cdot1\cdot1\cdot1=1\\~\\1^5=1\cdot1\cdot1\cdot1\cdot1=1\)

Apparently it works for any number.

Answer 9

Thanks