Question

Simplify tve radical expression
Show the steps

Answer 1

4x²y⁴

Explanation:

We are given:
`\sqrt[3}{(8x^3y^9)^2}`

Since,
`$ \sqrt[3]{a} = a^{(1)/(3)} $`.

Therefore, we get:

`$ (8x^3y^9)^{(2)/(3)} $`

Also, we have:

`$ (a^b)^c = a^(b.c) $`

⇒
`$ (2^3)^{(2)/(3)}. (x^3)^{(2)/(3)}. ((y^2)^3)^{(2)/(3)} $`

⇒
`$ 2^2 . x . (y^2)^2 $`

⇒
`$ 4. x. y^4 $` which is the required answer.