Question

Simplify:
${[\left\{\right(3^{5/2}\times 5^{3/4})÷2^{-5/4}\}÷\{16÷(5^2\times 2^{1/4}\times 3^{1/2}\left)\right\}]}^{1/5}$

Answer 1

$\left[\right\{(3^{5/2}\times 5^{3/4})÷2^{-5/4}\}÷\{16÷(5^2\times 2^{1/4}\times 3^{1/2})\}{]}^{1/5}$

$\Rightarrow {[\left\{\frac{3^{3/5}\times 5^{3/4}}{2^{-5/4}}\right\}÷\left\{\frac{16}{5^2\times 2^{1/4}\times 3^{1/2}}\right\}]}^{1/5}$

$\Rightarrow {[\{3^{5/2}\times 5^{3/4}\times 2^{5/4}\}÷\frac{16}{5^2\times 2^{1/4}\times 3^{1/2}}]}^{1/5}$

$\Rightarrow {\left[\frac{3^{5/2}\times 5^{3/4}\times 2^{5/4}\times 5^2\times 2^{1/2}\times 3^{1/2}}{16}\right]}^{1/5}$

$\Rightarrow {\left[\frac{3^3\times 5^{3/4+2}\times 2^{5/4+1/4}}{2^4}\right]}^{1/5}$

$\Rightarrow {\left[\frac{3^3\times 5^{11/4}\times 2^{3/2}}{2^4}\right]}^{1/5}$

$\Rightarrow {\left[\frac{3^3\times 5^{11/4}}{2^{(4-3/2)}}\right]}^{1/5}$ $\Rightarrow {\left[\frac{3^3\times 5^{11/4}}{2^{5/2}}\right]}^{1/5}$

$\Rightarrow \frac{(3^3\times 5^{11/4}{)}^{1/5}}{\sqrt{2}}$ $\Rightarrow \frac{3^{3/5}\times 5^{11/20}}{\sqrt{2}}$