Question

Which of the following is the simplest form of this expression?

Answer 1

Answer:

Simplest form is $a^{\frac{2}{15} }$.

Step-by-step explanation:

Given : $\frac{\sqrt[5]{a^{4}}}{\sqrt[3]{a^{2}}}$.

To find : Which of the following is the simplest form of this expression?

Solution: We have given :

$\frac{\sqrt[5]{a^{4}}}{\sqrt[3]{a^{2}}}$

By the radical rule $\sqrt[a]{b^{c} } = b^{\frac{c}{a}}$,

Then

$\frac{\sqrt[5]{a^{4}}}{\sqrt[3]{a^{2}}}$  = $\frac{a^{\frac{4}{5}}}{a^{\frac{2}{3}}}$.

⇒$a^{\frac{4}{5} -\frac{2}{3}}$.

⇒ $a^{\frac{12-10}{15} }$.

⇒ $a^{\frac{2}{15} }$.

Therefore, Simplest form is $a^{\frac{2}{15} }$.

Answer 2

The numerator could be written a⁴/⁵

The denominator could be written a²/³


Now solve  ( a⁴/⁵) / (a²/³) ==> a⁽⁴/⁵ ⁻²/³)  = a⁽²/¹⁵)

This is the simplest way