Question

in simipliest form what is(27a^-3)^-2/3

Answer 1

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