Question

Simplify
4/81x -8 x4

Answer 1

`(3)/(x)`

Explanation:

First simply the x terms under the square root

`x^(-8)x^4 = x^(-8 + 4) = x^(-4)\\\\`

`\sqrt[4]{81x^(-8)x{4}} = \sqrt[4]{81} \cdot\sqrt[4]{x^(-4)} \\\\\\ \sqrt[4]{81} = 3 \; since \; 3^4 = 81\\\\\sqrt[4]{x^(-4)} = (x^(-4))^{(1)/(4) } = x^(-1) = (1)/(x) \\\\\\`

So

`\sqrt[4]{81x^(-8)x{4}} = (3)/(x)`