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Math Help - Index laws

  1. #1
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    Index laws

    Questions from my textbook i had trouble with, thanks

    Simplify,
    1.i (4x^2y^2)^2 + 2(x^2y)^4

    ii. (x^2+y^2)/x^-2+y^-2

    2.Find n
    i (3^(n-2)) / (9^(2-n)) = 27

    ii 2^(n-4) = 8^(4-n)

    iii. 8^(6n+2) = 8^(4n-1)

    iv. (27*(3^n))^n = 27^n * 3^(1/4)

    3. Find x
    16^x = 1024

    Thanks alot
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  2. #2
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    Quote Originally Posted by chaneliman View Post
    Questions from my textbook i had trouble with, thanks

    ...

    2.Find n
    i (3^(n-2)) / (9^(2-n)) = 27

    ...

    3. Find x
    16^x = 1024

    ...
    \frac{3^{n-2}}{9^{2-n}}=27 Transform all powers to powers with base 3:

    \frac{3^{n-2}}{(3^2)^{2-n}}=3^3

    3^n \cdot \frac1{3^2} \cdot \frac1{3^4} \cdot 3^{2n}=3^3~\implies~3^{3n} = 3^{9}~\implies~\boxed{n=3}


    16^x = 1024 Transform the powers into powers of base 2:

    (2^4)^x=2^{10}~\implies~4x = 10~\implies~x = \frac52
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