Simplify

$\left(\frac{3125}{243}\right)^{\frac{4}{5}}$

$=\left(\frac{5 \times 5 \times 5 \times 5 \times 5}{3 \times 3 \times 3 \times 3 \times 3}\right)^{\frac{4}{5}}$

$=\left(\frac{5^{5}}{3^{5}}\right)^{\frac{4}{5}}$

$=\left[\left(\frac{5}{3}\right)^{5}\right]^{\frac{4}{5}}$

$\left[\left(\frac{x}{y}\right)^{a}=\frac{x^{a}}{y^{a}}\right]$

$\left[\left(x^{a}\right)^{b}=x^{a b}\right]$

$=\left(\frac{5}{3}\right)^{5 \times \frac{4}{5}}$

$=\left(\frac{5}{3}\right)^{4}$

$=\frac{5 \times 5 \times 5 \times 5}{3 \times 3 \times 3 \times 3}$

$=\frac{625}{81}$