Question

Mark (✓) against the correct answer
${\left\{{\left(\frac{1}{3}\right)}^2\right\}}^4=?$

(a) ${\left(\frac{1}{3}\right)}^6$
(b) ${\left(\frac{1}{3}\right)}^8$
(c) ${\left(\frac{1}{3}\right)}^{16}$
(d) ${\left(\frac{1}{3}\right)}^{24}$

Answer 1

(b) ${\left(\frac{1}{3}\right)}^8$

${\left\{{\left(\frac{1}{3}\right)}^2\right\}}^4={\left(\frac{1}{3}\right)}^{2\times 4}={\left(\frac{1}{3}\right)}^8$ $\left[s\mathrm{ince}{\left\{{\left(\frac{\mathrm{a}}{\mathrm{b}}\right)}^{\mathrm{m}}\right\}}^{\mathrm{n}}={\left(\frac{\mathrm{a}}{\mathrm{b}}\right)}^{\mathrm{mn}}\right]$