Question

For a non-zero integer $x$, ${\left(x^4\right)}^{-3}$ is equal to:

• A. $x^{12}$
• B. $x^{-12}$
• C. $x^{64}$
• D. $x^{-64}$

Answer 1

The correct option is B

$x^{-12}$

Explanation for the correct option:

$\begin{array}{rcl}{\left(x^4\right)}^{-3}& =& {\left(x\right)}^{4\times \left(-3\right)}\left[\because {\left(a^m\right)}^{\mathbf{n}}\mathbf{=}{\mathit{a}}^{\mathbf{m}\mathbf{\times }\mathbf{n}}\right]\\ \therefore {\left(x^4\right)}^{-3}& =& x^{-12}\end{array}$

Hence, the value of ${\left(x^4\right)}^{-3}$ is $x^{-12}$