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Math Help - need help with indices simplify

  1. #1
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    need help with indices simplify

    simplify
    (9 x 3^2)^3 / (3 x 27 ) ^2

    similar

    (16 x 4)^2 / (2 x 8)^3

    got stuck on these if some could help out and explain working would be great
    I tried changing them to the same base so i could apply rules but stull having probs
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  2. #2
    MHF Contributor red_dog's Avatar
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    The numerator:

    9=3^2

    9\cdot 3^2=3^2\cdot3^2=3^4

    (9\cdot 3^2)^3=(3^4)^3=3^{12}

    The denominator:

    27=3^3

    3\cdot 27=3\cdot 3^3=3^4

    (3\cdot 27)^2=(3^4)^2=3^8

    Now, \frac{(9\cdot 3^2)^3}{(3\cdot 27)^2}=\frac{3^{12}}{3^8}=3^{12-8}=3^4=81

    Can you do the other in a similar way?
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  3. #3
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    yes i see now thanks alot
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