Answer:
[tex]z^{\frac{1}{5} } and \sqrt[5]{z}[/tex]
Step-by-step explanation:
Given the expression [tex]z^{0.2}[/tex], the following is equivalent to the expression;
First we convert the decimal to a fraction
[tex]z^{0.2}\\= z^{\frac{2}{10} }\\\= z^{\frac{1}{5} }[/tex]
According to one of the laws of indices;
[tex]a^{\frac{m}{n} }= \sqrt[n]{m}[/tex]
Applying this to the resulting indices above;
[tex]z^{\frac{1}{5} } = (\sqrt[5]{z})^{1} \\= \sqrt[5]{z}[/tex]
Based on the calculation above, the expressions that is equivalent to [tex]z^{0.2}[/tex] are [tex]z^{\frac{1}{5} } and \sqrt[5]{z}[/tex]