Question

Simplify the following expression.

$(h^{-2}{)}^2\times (f^{2}h{)}^{3/2}÷(f^6{h}^{-3}{)}^{1/6}$

Answer 1

$\frac{\frac{1}{(h^2{)}^2}\times (f^2{)}^{\frac{3}{2}}{h}^{\frac{3}{2}}}{(f^6{)}^{\frac{1}{6}}\times \frac{1}{(h^3{)}^{\frac{1}{6}}}}$

$=\frac{\frac{1}{h^4}\times f^3\times h^{\frac{3}{2}}\times h^{\frac{1}{2}}}{f}$

$=\frac{f^2\times h^2}{h^4}$

$=\frac{f^2}{h^2}$

Answer: $h^{-2}{f}^2$