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,

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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)

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Thành Công 4 years 2021-09-04T07:00:32+00:00 2 Answers 5 views 0

Answers ( )

  1. Doris
    0
    2021-09-04T07:01:50+00:00
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    Part A

    Answer: x = 0

    ——————–

    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.

    =========================================

    Part B

    Answer: x = any real number you want

    ——————–

    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.

  2. thienhuong
    0
    2021-09-04T07:02:10+00:00
    Reply

    Answer:

               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

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