Question

What is the simplest form of ^4√81x^8y^5?

Answer 1

`3x^2y\sqrt[4]{y}`

Explanation:

We have been given the radical expression
`\sqrt[4]{81x^8y^5}`

We can rewrite the terms inside the radical as:

`81=3^4\\x^8=(x^2)^4\\y^5=y^4\cdot y`

Hence, the expression will become

`\sqrt[4]{3^4\cdot(x^2)^4\cdot y^4\cdot y}`

Apply the exponent rule:
`\sqrt[n]{x^n}=x`

`=3\cdotx^2\cdot y\sqrt[4]{y}\\\\=3x^2y\sqrt[4]{y}`

Hence, the simplified expression is
`3x^2y\sqrt[4]{y}`

Answer 2

`\sqrt[4]{81 x^(8) y^(5)} = \sqrt[4]{(3 x^(2) y)^(4) y} = 3 x^(2) y \sqrt[4]{y}`