Question

Part A: If (2⁶)ˣ = 1, what is the value of x? Explain your answer. (5 points)

Part B: If (5⁰ )ˣ = 1, what are the possible values of x? Explain your answer. (5 points)

Answer 1

# Part A

`\sf { ({2}^(6) )}^(x) = 1`

• Simplify the expression by multiplying exponents

`\sf {2}^(6x) = 1`

• Write 1 as a power of 2

`\sf {2}^(6x) = {2}^(0)`

• Since the base are same equate the powers

`\sf 6x = 0`

• Solve for x

`\boxed{ \underline{ \underline{ \tt \: x = 0}}}`

# Part B

`\sf \: { ({5}^(0)) }^(x) = 1`

• Simplify the expression by multiplying exponents

`\sf \: {5}^(0) = 1`

`\sf \: 1 = 1`

`\boxed{ \underline{ \underline{ \tt \: x = any \: real \: number}}}`