Question

Simpllfy : $\frac{{13}^{\frac{1}{5}}}{{13}^{\frac{1}{3}}}$

• A. ${13}^{\frac{2}{15}}$
• B. ${13}^{\frac{8}{15}}$
• C. ${13}^{\frac{1}{3}}$
• D. ${13}^{\frac{-2}{15}}$

Answer 1

The correct option is D ${13}^{\frac{-2}{15}}$

$\frac{{13}^{\frac{1}{5}}}{{13}^{\frac{1}{3}}}$ $\Rightarrow$ $(13{)}^{\frac{1}{5}-\frac{1}{3}}$ $[\because \frac{x^m}{x^n}=x^{m-n}]$

$\Rightarrow$ $(13{)}^{\frac{3-5}{15}}$

$\Rightarrow$ ${13}^{\frac{-2}{15}}$

$\therefore$ $\frac{{13}^{\frac{1}{5}}}{{13}^{\frac{1}{3}}}={13}^{\frac{-2}{15}}$