Question

PLEASE HELP 30 points

Select the correct answer.
Simplify the expression.
$768x845
OA. 4x2y $34
B. 4x2y2 3x2y
O c. 2xy2 +2x
OD. 4r3y +3.72
Reset

Answer 1

A

Explanation:

Given expression:

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

Using rule
`√(ab) =√(a) \cdot √(b)`

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

Prime factorization of 768:

`=\sqrt[4]{2^8\cdot3} \cdot \sqrt[4]{x^8} \cdot\sqrt[4]{y^5}`

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

Using rule
`a^(b+c)=a^ba^c` :

`=\sqrt[4]{2^8} \cdot \sqrt[4]{3} \cdot \sqrt[4]{x^8} \cdot\sqrt[4]{y^(4+1)}`

`=\sqrt[4]{2^8} \cdot \sqrt[4]{3} \cdot \sqrt[4]{x^8} \cdot\sqrt[4]{y^4y^1}}`

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

Using rule
`\sqrt[a]{b^c} =b^{(c)/(a)}` :

`=2^(\frac84)} \cdot \sqrt[4]{3} \cdot x^(\frac84)\cdot y^(\frac44) \cdot \sqrt[4]{y}`

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

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

Gather like terms:

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

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