Question

Simplify:

iii. $\sqrt[3]{3(343{)}^{-2}}$

Answer 1

To simplify: $\sqrt[3]{3(343{)}^{-2}}$

$=(343{)}^{\frac{-2}{3}}$ $\{\because \sqrt[n]{n{a}^m}=a^{\frac{m}{n}}\}$

$=(7^3{)}^{\frac{-2}{3}}$

$=7^{3\times \frac{-2}{3}}$ $\{\because (a^m{)}^n=a^{mn}\}$

$=7^{-2}$

$=\frac{1}{7^2}$ $\{\because a^{-m}=\frac{1}{a^m}\}$

$=\frac{1}{49}$

Therefore, $\sqrt[3]{3{343}^{-2}}=\frac{1}{49}$