Question

PLEASE HELP (85 points)

Part A: If (7^2)^x = 1, what is the value of x? Explain your answer. (5 points)
Part B: If (7^0)^x = 1, what are the possible values of x? Explain your answer. (5 points)

Answer 1

Part A: If (7^2)^x = 1, ⇒ x=0

Part B: If (7^0)^x = 1 ⇒ x∈R

Step-by-step explanation:

Part A: If (7^2)^x = 1, what is the value of x?

Any number (except 0) to the power of 0 gives 1 (Law of Exponents)

And there is no other power that gives 1 if base is not 1

7^2≠1 so x must be 0

Part B: If (7^0)^x = 1, what are the possible values of x?

7^0 = 1 and 1 to any power always gives 1, so no mater what x we choose we always get 1

Answer 2

Part A

Answer: x = 0

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Step-by-step explanation:

Anything to the 0th power exponent is equal to 1, as long as the base isn't 0 itself. So (7^2)^x = (7^2)^0 = 1.

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Part B

Answer: x = any real number you want

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Step-by-step explanation:

The 7^0 evaluates to 1, due to the rule discussed back in part A.

This means (7^0)^x = 1 becomes 1^x = 1. We can replace x with any real number and we would have 1^x always evaluate to 1.

For instance, if x = 3, then 1^x = 1^3 = 1*1*1 = 1. Multiplying out a string of 1's leads to 1 as the final result. We could even have 1^0 and we'd still evaluate to 1.