Question

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

Answer 1

B!!!!!!!!!

Explanation:

Answer 2

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

EXPLANATION

We want to simplify:

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

We can split the radical sign to obtain:

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

Or

`\sqrt[4]{81} * \sqrt[4]{ {x}^(8) } * \sqrt[4]{ {y}^(4) * y}`

`\sqrt[4]{81} * \sqrt[4]{ {x}^(8) } * \sqrt[4]{ {y}^(4)} * \sqrt[4]{y}`

`\sqrt[4]{ {3}^(4) } * \sqrt[4]{ {x}^(8) } * \sqrt[4]{ {y}^(4)} * \sqrt[4]{y}`

Recall that:

`\sqrt[n]{ {a}^(m) } = {a}^{ (m)/(n) }`

`{3}^{4 * (1)/(4) } * {x}^{8 * (1)/(4) } * {y}^{4 * (1)/(4) }* \sqrt[4]{y}`

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