which expression is equivalent to $\\left(\\frac{1}{z^{3/5}}\\right)^{-1/5}$?\na. $z^{3/25}$\nb…

Explanation:

Step1: Apply negative - exponent rule

Recall that $\left(\frac{a}{b}\right)^{-n}=\left(\frac{b}{a}\right)^{n}$. So, $\left(\frac{1}{z^{3/5}}\right)^{-1/5}=(z^{3/5})^{1/5}$.

Step2: Apply power - of - a - power rule

The power - of - a - power rule states that $(a^{m})^{n}=a^{mn}$. Here, $a = z$, $m=\frac{3}{5}$, and $n = \frac{1}{5}$. Then $(z^{3/5})^{1/5}=z^{\frac{3}{5}\times\frac{1}{5}}=z^{3/25}$.

Answer:

A. $z^{3/25}$