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

1. anonymous

a^18/2187

2. anonymous

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

3. anonymous

4. anonymous

I think my solution is valid if a is positive.

5. amistre64

even if a is negative its fine

6. anonymous

Thank you very much!