Question

For a non-zero rational number $z$, ${\left(z^{-2}\right)}^3$ is equal to:

• A. $z^6$
• B. $z^{-6}$
• C. $z^1$
• D. $z^4$

Answer 1

The correct option is B

$z^{-6}$

Explanation for the correct option:

$\begin{array}{rcl}{\left(z^{-2}\right)}^3& =& {\left(z\right)}^{\left(-2\right)\times \left(3\right)}\left[\because {\left(a^m\right)}^{\mathbf{n}}\mathbf{=}{\mathit{a}}^{\mathbf{m}\mathbf{\times }\mathbf{n}}\right]\\ \therefore {\left(z^{-2}\right)}^3& =& z^{-6}\end{array}$

Hence, the correct option is option B