Question

Simplify:

${\left[\right(64{)}^{-3}\times \left(81{)}^{-\frac{9}{4}}\right]}^{-\frac{1}{9}}$

Answer 1

Now,

${\left[\right(64{)}^{-3}\times \left(81{)}^{-\frac{9}{4}}\right]}^{-\frac{1}{9}}$

$={\left[\right(4^3{)}^{-3}\times \left(3^4{)}^{-\frac{9}{4}}\right]}^{-\frac{1}{9}}$

$={\left[\right(4{)}^{-9}\times \left(3{)}^{-9}\right]}^{-\frac{1}{9}}$

$={\left[\right(4)\times (3\left)\right]}^{-\frac{1}{9}\times (-9)}$

$=4\times 3$

$=12$.