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write (27a^-9)^-2/3 in simplest form please help me ive been stuck on this for like 20 minutes now

  • 10 months ago
  • 10 months ago

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  1. brandeejo
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    a^18/2187

    • 10 months ago
  2. giolefpatceid
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    \[(27a^{-9})^{-\frac{2}{3}} = 27^{-\frac{2}{3}}(a^{-9})^{-\frac{2}{3}} = (3^3)^{-\frac{2}{3}}(a^{-9})^{-\frac{2}{3}}\] \[=3^{-3\frac{2}{3}}a^{-9\frac{-2}{3}} = 3^{-2}a^{6} = \frac{1}{3^2}a^6= \frac{1}{9}a^6\]

    • 10 months ago
  3. giolefpatceid
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    @amistre64 Could you please validate my solution? Thank you in advance!

    • 10 months ago
  4. giolefpatceid
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    I think my solution is valid if a is positive.

    • 10 months ago
  5. amistre64
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    even if a is negative its fine

    • 10 months ago
  6. giolefpatceid
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    Thank you very much!

    • 10 months ago
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