Question

$[{(-3)}^2{]}^3$ is equal to

• A. ${(-3)}^8$
• B. ${(-3)}^6$
• C. ${(-3)}^5$
• D. ${(-3)}^{23}$

Answer 1

The correct option is B

${(-3)}^6$

Finding $[{(-3)}^2{]}^3$

For any non-zero integers $\mathrm{a}$ and $\mathrm{b}$ whole numbers $\mathrm{m}$ and $\mathrm{n}$, we have

${\left(a^m\right)}^n=a^{mn}$

So, putting $a=-3,m=2,n=3$, we get

$\begin{array}{rcl}{\left(a^m\right)}^n& =& a^{mn}\\ \Rightarrow [{(-3)}^2{]}^3& =& -3^{(2\times 3)}\\ \Rightarrow [{(-3)}^2{]}^3& =& -3^6\end{array}$

$\therefore$The correct option is B.