Question

The value of${\left(\frac{-2}{3}\right)}^4$ is equal to

• A. $\frac{16}{81}$
• B. $\frac{81}{16}$
• C. $\frac{-16}{81}$
• D. $\frac{-81}{16}$

Answer 1

The correct option is A

$\frac{16}{81}$

Find the value of${\left(\frac{-2}{3}\right)}^4$

By using the law of exponent,

${\left(\frac{\mathrm{a}}{\mathrm{b}}\right)}^{\mathrm{m}}=\frac{{\mathrm{a}}^{\mathrm{m}}}{{\mathrm{b}}^{\mathrm{m}}}$

$\begin{array}{rcl}{\left(\frac{-2}{3}\right)}^4& =& \left(\frac{-2}{3}\right)\times \left(\frac{-2}{3}\right)\times \left(\frac{-2}{3}\right)\times \left(\frac{-2}{3}\right)\\ & =& \frac{16}{81}\\ \therefore {\left(\frac{-2}{3}\right)}^4& =& \frac{16}{81}\end{array}$

Hence, the correct option is A.