Use repeated multiplication to compute ${\left(\frac{2}{3}\right)}^3$.

Which statement shown below is true about distributing exponents?

Simplify ${\left(\frac{2x}{3x}\right)}^2$.

What is the value of ${\left({\frac{a}{b}}^{}\right)}^0$ for nonzero $a$ and $b$?

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.