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Need some extra help on rational exponents...?

I've tried to solve these two problems over 20 times now and I cannot figure out my mistake. I'm not one to just ask my homework questions on line because I'm lazy - I tried for these, I swear!

1) (8a^-6)^-2/3

2) (9n^-5)^-3/2

I know that the answer to 1 is supposed to be (a^4)/4. I've gotten the answer 4/(a^4) but do not see which inverse I am messing up to get to the real answer.

Thanks for your time, Nathan S.

2 Answers

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  • Anonymous
    1 decade ago
    Favorite Answer

    1.(8/a^6)^-2/3

    (cube root)(8/a^6)^-2

    (cube root)(a^12/64)

    a^4/4

    2. (9n^-5)^-3/2

    (9/n^5)^-3/2

    √(9/n^5)^-3

    √(n^15/729)

    n^7√n/27

  • 1 decade ago

    hello, dear.

    okay, for the first one, separate each term & work them individually:

    (8) ^ -2/3 & (a ^ -6) ^ -2/3

    for the (a ^ -6) ^ -2/3 you just multiply the exponents, or powers together to get an answer of:

    a ^ 4

    & for the 8 ^ -2/3, just take it to the denominator to make the exponent positive:

    a ^ 4

    -------

    8 ^ 2/3

    a ^ 4

    --------

    4

    for the second problem, repeat the same exact steps.

    hope this helps! good luck!

    Source(s): 99% in AP calculus. ; ]
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