For what value of a does (one-ninth) Superscript a + 1 Baseline = 81 Superscript a + 1 Baseline times 27 Superscript 2 minus a?

Question

For what value of a does (one-ninth) Superscript a + 1 Baseline = 81 Superscript a + 1 Baseline times 27 Superscript 2 minus a?

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Isabella 4 weeks 2021-09-21T04:38:49+00:00 2 Answers 0

Answers ( )

    0
    2021-09-21T04:39:51+00:00

    Answer:

    a = -4

    Step-by-step explanation:

    The equation to solve for “a” is:

    (\frac{1}{9})^{a+1}=81^{a+1}*27^{2-a}

    The first step is to convert all of them to same bases.

    9, 81, and 27, all can be expressed in base 3, lets do this:

    (\frac{1}{9})^{a+1}=81^{a+1}*27^{2-a}\\(3^{-2})^{a+1}=(3^4)^{a+1}*(3^3)^{2-a}

    We can use the property: (a^b)^c=a^{bc} to simplify further:

    (3^{-2})^{a+1}=(3^4)^{a+1}*(3^3)^{2-a}\\3^{-2a-2}=3^{4a+4}*3^{6-3a}

    The right side has 2 same bases multiplied, we can simplify this using the property:  a^x * a^y = a^{x+y}

    Thus, we have:

    3^{-2a-2}=3^{4a+4}*3^{6-3a}\\3^{-2a-2}=3^{4a+4+6-3a}}\\3^{-2a-2}=3^{a+10}

    Now, both sides have same base, so exponents would be equal. Now lets equate and solve for “a”:

    3^{-2a-2}=3^{a+10}\\-2a-2=a+10\\3a=-12\\a=-4

    So,

    a = -4

    0
    2021-09-21T04:40:44+00:00

    Answer:

    A) -4

    Step-by-step explanation:

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45:7+7-4:2-5:5*4+35:2 =? ( )