Question

Simplify the expression. Someone help please...

Answer 1

`\sqrt[4]{768x^8y^5} = 4x^2y \sqrt[4]{3y}`

Explanation:

Given

`\sqrt[4]{768x^8y^5}`

Required

Simplify

We have:

`\sqrt[4]{768x^8y^5}`

Expand 768

`\sqrt[4]{768x^8y^5} = \sqrt[4]{256 * 3 * x^8y^5}`

Split

`\sqrt[4]{768x^8y^5} = \sqrt[4]{256} * \sqrt[4]{3 * x^8y^5}`

`\sqrt[4]{256} = 4`

So, we have:

`\sqrt[4]{768x^8y^5} = 4* \sqrt[4]{3 * x^8y^5}`

Expand y^5

`\sqrt[4]{768x^8y^5} = 4* \sqrt[4]{3 * x^8*y *y^4}`

Rewrite as:

`\sqrt[4]{768x^8y^5} = 4* \sqrt[4]{3*y * x^8 *y^4}`

`\sqrt[4]{768x^8y^5} = 4* \sqrt[4]{3y * x^8 *y^4}`

Split

`\sqrt[4]{768x^8y^5} = 4* \sqrt[4]{3y} * \sqrt[4]{x^8 *y^4}`

Apply the following law of indices

`\sqrt[a]{b} = b^(1)/(a)`

`\sqrt[4]{768x^8y^5} = 4* \sqrt[4]{3y} * (x^8 *y^4)^(1)/(4)`

Expand

`\sqrt[4]{768x^8y^5} = 4* \sqrt[4]{3y} * x^{8*(1)/(4)} *y^{4*(1)/(4)}`

`\sqrt[4]{768x^8y^5} = 4* \sqrt[4]{3y} * x^2y`

Rewrite as:

`\sqrt[4]{768x^8y^5} = 4* x^2y* \sqrt[4]{3y}`

`\sqrt[4]{768x^8y^5} = 4x^2y \sqrt[4]{3y}`