Question:
After simplification, $\frac{13^{\frac{1}{5}}}{13^{\frac{1}{3}}}$ is
(a) $13^{\frac{2}{15}}$
(b) $13^{\frac{8}{15}}$
(c) $13^{\frac{1}{3}}$
(d) $13^{\frac{-2}{15}}$
Solution:
$\frac{13 \frac{1}{5}}{13^{\frac{1}{3}}}$
$=13^{\frac{1}{5}-\frac{1}{3}} \quad\left(\frac{x^{a}}{x^{b}}=x^{a-b}\right)$
$=13^{\frac{3-5}{15}}$
$=13^{\frac{-2}{15}}$
Hence, the correct answer is option (d).
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