Question

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

Answer 1

a^18/2187

Answer 2

\[(27a^{-9})^{-\frac{2}{3}} = 27^{-\frac{2}{3}}(a^{-9})^{-\frac{2}{3}} = (3^3)^{-\frac{2}{3}}(a^{-9})^{-\frac{2}{3}}\]
\[=3^{-3\frac{2}{3}}a^{-9\frac{-2}{3}} = 3^{-2}a^{6} = \frac{1}{3^2}a^6= \frac{1}{9}a^6\]

Answer 3

@amistre64 Could you please validate my solution? Thank you in advance!

Answer 4

I think my solution is valid if a is positive.

Answer 5

even if a is negative its fine

Answer 6

Thank you very much!