Question

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

Answer 1

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

Answer 2

Simplest form is
`a^{(2)/(15) }`.

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^{(c)/(a)}`,

Then

`\frac{\sqrt[5]{a^(4)}}{\sqrt[3]{a^(2)}}` =
`\frac{a^{(4)/(5)}}{a^{(2)/(3)}}`.

⇒
`a^{(4)/(5) -(2)/(3)}`.

⇒
`a^{(12-10)/(15) }`.

⇒
`a^{(2)/(15) }`.

Therefore, Simplest form is
`a^{(2)/(15) }`.