Question

Simplify the expression. Someone help please...

Answer 1

Answer:

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

Step-by-step 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

$\sqrt[a]{b} = b^\frac{1}{a}$

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

Expand

$\sqrt[4]{768x^8y^5} = 4* \sqrt[4]{3y} * x^{8*\frac{1}{4}} *y^{4*\frac{1}{4}}$

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

Rewrite as:

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

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