To simplify the given expression [tex]\(\left(\frac{1}{z^{3 / 5}}\right)^{-1 / 5}\)[/tex], we can follow a series of algebraic steps.
1. Start with the inner part of the expression: [tex]\(\frac{1}{z^{3 / 5}}\)[/tex].
2. Recognize that [tex]\(\frac{1}{z^{3 / 5}}\)[/tex] is the same as [tex]\(z^{-3 / 5}\)[/tex]:
[tex]\[
\frac{1}{z^{3 / 5}} = z^{-3 / 5}
\][/tex]
3. Now consider the outer exponent [tex]\(-1 / 5\)[/tex]:
[tex]\[
\left(z^{-3 / 5}\right)^{-1 / 5}
\][/tex]
4. Apply the property of exponents [tex]\((a^m)^n = a^{m \cdot n}\)[/tex]:
[tex]\[
\left(z^{-3 / 5}\right)^{-1 / 5} = z^{\left(-3 / 5 \cdot -1 / 5\right)}
\][/tex]
5. Multiply the exponents:
[tex]\[
-3 / 5 \cdot -1 / 5 = \frac{3}{25}
\][/tex]
6. Thus, we get:
[tex]\[
z^{3 / 25}
\][/tex]
Hence, the equivalent expression is:
[tex]\[
z^{3 / 25}
\][/tex]
The correct answer is:
A. [tex]\(z^{3 / 25}\)[/tex]
