Question

Write ${\left(\frac{1}{9}\right)}^{\frac{-1}{2}}\times (64{)}^{\frac{-1}{3}}$ as a rationalnumber.

Answer 1

${\left(\frac{1}{9}\right)}^{\frac{-1}{2}}\times (64{)}^{\frac{-1}{3}}={\left[{\left(\frac{1}{3}\right)}^2\right]}^{\frac{-1}{2}}\times (4^3{)}^{\frac{-1}{3}}={\left(\frac{1}{3}\right)}^{2\times \left(\frac{-1}{2}\right)}\times 4^{(3\times \frac{-1}{3})}={\left(\frac{1}{3}\right)}^{-1}\times 4^{-1}=3\times \frac{1}{4}=\frac{3}{4}$