Simplify the expression ${\left(\frac{p}{2}\right)}^4$. Use distribution of the exponent and simplify any numerical powers.

Compute and simplify ${(-\frac{2}{5})}^3$.

Which statement shown below is true about distributing exponents?

A rectangular garden's linear dimensions are scaled by a factor of $\frac{3}{4}$. If the original area was $200{\text{cm}}^2$, compute the new area by applying the appropriate power of a quotient rule.

Given the equation $(\frac{2x}{5y}{)}^3=\frac{16}{125}$ with $x$ and $y$ nonzero, find $\frac{x}{y}$.