Question

Prove that:
$4^{\frac{1}{3}}\times [2^{\frac{1}{3}}\times 3^{\frac{1}{2}}]÷9^{\frac{1}{4}}=2$.

Answer 1

LHS=$4^{\frac{1}{3}}\times [2^{\frac{1}{3}}\times 3^{\frac{1}{2}}]÷9^{\frac{1}{4}}$

$\Rightarrow \frac{(2^2{)}^{\frac{1}{3}}\times \left[2^{\frac{1}{3}}\right]\times (3^{\frac{1}{2}})}{(3^2{)}^{\frac{1}{4}}}$

$\Rightarrow \frac{2^{\frac{2}{3}}\times 2^{\frac{1}{3}}\times 3^{\frac{1}{2}}}{3^{\frac{1}{2}}}=2^{\frac{2}{3}+\frac{1}{3}}$
$=2^1=2$=RHS
Hence, proved.