Which expressions are equivalent to the one below? Check all that apply. 9^x ОА. 9. 9x – 1 В. 9. 9х+1 с. 36/4^x D.x

Question

Which expressions are equivalent to the one below? Check all that apply.
9^x
ОА. 9. 9x – 1
В. 9. 9х+1
с. 36/4^x
D.x^5
Е. 36

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Natalia 1 week 2021-09-11T00:33:05+00:00 1 Answer 0

Answers ( )

    0
    2021-09-11T00:34:50+00:00

    Answer:

    A. 9\cdot 9^{x-1}

    C. (\frac{36}{4})^x

    Step-by-step explanation:

    Given:

    The given expression is 9^x

    Let us simplify each choice and check whether they simplify to 9^x or not.

    Choice A:

    9\cdot 9^{x-1}

    We use the law of indices: a^m\cdot a^n=a^{m+n}

    Therefore, 9^1\cdot 9^{x-1}=9^{1+x-1}=9^x=9^x(True)

    Choice B:

    9\cdot 9^{x+1}

    We use the law of indices: a^m\cdot a^n=a^{m+n}

    Therefore, 9^1\cdot 9^{x+1}=9^{1+x+1}=9^{x+2}\ne 9^x(False)

    Choice C:

    (\frac{36}{4})^{x}

    We simplify the fraction inside the parenthesis. So,

    (\frac{36}{4})^{x}=(9)^x=9^x(True)

    Choice D:

    x^5\ne 9^x

    Choice E:

    36\ne 9^x

    Therefore, the correct options are A and C.

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