Answer:
[tex]\sqrt[4]{768x^8y^5} = 4x^2y \sqrt[4]{3y}[/tex]
Step-by-step explanation:
Given
[tex]\sqrt[4]{768x^8y^5}[/tex]
Required
Simplify
We have:
[tex]\sqrt[4]{768x^8y^5}[/tex]
Expand 768
[tex]\sqrt[4]{768x^8y^5} = \sqrt[4]{256 * 3 * x^8y^5}[/tex]
Split
[tex]\sqrt[4]{768x^8y^5} = \sqrt[4]{256} * \sqrt[4]{3 * x^8y^5}[/tex]
[tex]\sqrt[4]{256} = 4[/tex]
So, we have:
[tex]\sqrt[4]{768x^8y^5} = 4* \sqrt[4]{3 * x^8y^5}[/tex]
Expand y^5
[tex]\sqrt[4]{768x^8y^5} = 4* \sqrt[4]{3 * x^8*y *y^4}[/tex]
Rewrite as:
[tex]\sqrt[4]{768x^8y^5} = 4* \sqrt[4]{3*y * x^8 *y^4}[/tex]
[tex]\sqrt[4]{768x^8y^5} = 4* \sqrt[4]{3y * x^8 *y^4}[/tex]
Split
[tex]\sqrt[4]{768x^8y^5} = 4* \sqrt[4]{3y} * \sqrt[4]{x^8 *y^4}[/tex]
Apply the following law of indices
[tex]\sqrt[a]{b} = b^\frac{1}{a}[/tex]
[tex]\sqrt[4]{768x^8y^5} = 4* \sqrt[4]{3y} * (x^8 *y^4)^\frac{1}{4}[/tex]
Expand
[tex]\sqrt[4]{768x^8y^5} = 4* \sqrt[4]{3y} * x^{8*\frac{1}{4}} *y^{4*\frac{1}{4}}[/tex]
[tex]\sqrt[4]{768x^8y^5} = 4* \sqrt[4]{3y} * x^2y[/tex]
Rewrite as:
[tex]\sqrt[4]{768x^8y^5} = 4* x^2y* \sqrt[4]{3y}[/tex]
[tex]\sqrt[4]{768x^8y^5} = 4x^2y \sqrt[4]{3y}[/tex]
