Simplify the expresion

Question

I want to simplify this expression

$ a^{\frac{1}{6}} \sqrt[3]{a} - \frac{a^{\frac{2}{7}}}{\sqrt{a}} $

This has to give me $ \sqrt{a} - \sqrt[21]{a^5} $ , but I don't know how to get to that result

Answer 1

From your given equation,

$a^{\frac{1}{6}+\frac{1}{3}}$- $a^{\frac{2}{7}-\frac{1}{2}}$

= $a^{\frac{1}{2}}$ - $a^{-\frac{3}{14}}$

I think there's an error with the question/answer

Answer 2

$a^{\frac{1}{6}}\sqrt[3]{a}=a^{\frac{1}{6}}a^{\frac{1}{3}}=\sqrt{a}$

$\frac{a^{\frac{2}{7}}}{\sqrt{a}}=\frac{a^\frac{2}{7}}{a^{\frac{1}{2}}}=a^{\frac{2}{7}}a^{-\frac{1}{2}}=a^{-\frac{3}{14}}$

so it is $\sqrt{a}-\frac{1}{\sqrt[14]{a^3}}$

$\frac{1}{\sqrt[14]{a^3}}\neq \sqrt[21]{a^5}$