Question

simplify (3a^-1b^2)^-2 is 9a^2b^4 correct?

Answer 1

a^2/9b^4

Answer 2

\[(3a^{-1}b^2)^{-2}=3^{-2}a^{2}b^{-4}=\frac{a^2}{9b^4}\]

Answer 3

thank you!

Answer 4

but why is 9 on bottom?

Answer 5

3^{-2}=1/(3^2)=1/9

Answer 6

\[(3^1a^{-1}b^2)^{-2}=3^{1 \cdot -2}a^{-1 \cdot -2}b^{2 \cdot -2}=3^{-2}a^{2}b^{-4}\]

Answer 7

\[=\frac{1}{3^2} \cdot a^2 \cdot \frac{1}{b^4}=\frac{a^2}{3^2b^4}=\frac{a^2}{9b^4}\]

Answer 8

perfect! thank you!