N the numerical sentence below, A = 8, D =1/2 , and F =1/4 . What are the values B, C, and E if the sentence below is equivalent to the nume

Question

N the numerical sentence below, A = 8, D =1/2 , and F =1/4 . What are the values B, C, and E if the sentence below is equivalent to the numerical sentence, 2 × 4 = 8?

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Trúc Chi 4 years 2021-08-24T13:59:50+00:00 1 Answers 99 views 0

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  1. thuthao
    0
    2021-08-24T14:01:33+00:00
    Reply

    Answer:

    B = \frac{1}{3}

    C = 16

    E = 4096

    Step-by-step explanation:

    Given

    A^B * C^D = E^F — Missing from the question

    2*4 = 8

    A = 8

    D = \frac{1}{2}

    F = \frac{1}{4}

    Required: Find B, C and E


    Substitute values for A, D and F in A^B * C^D = E^F

    8^B * C^{\frac{1}{2}} = E^{\frac{1}{4}}

    Compare the above expression to: 2*4 = 8

    We have:

    8^B = 2

    C^{\frac{1}{2}} = 4

    E^{\frac{1}{4}} = 8

    In 8^B = 2

    Express 8 as a 2^3

    2^{3B }= 2^1

    Cancel out 2

    3B = 1

    B = \frac{1}{3}

    In C^{\frac{1}{2}} = 4

    Express 4 as 16^{\frac{1}{2}}

    C^{\frac{1}{2}} = 16^{\frac{1}{2}}

    The exponents cancel out

    C = 16

    In E^{\frac{1}{4}} = 8

    Express 8 as 4096^{\frac{1}{4}}

    E^{\frac{1}{4}} = 4096^{\frac{1}{4}}

    The exponents cancel out

    E = 4096

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