Question

simplify the radical expression. $sqrt4{81x^{4}}$ write your answer in the form a, $sqrt4{b}$, or a$sqrt4{b}$ with constants or expressions in x. use at most one radical and at most one absolute value symbol in your expression

Explanation:

Step1: Rewrite 81 as a 4th power

$81 = 3^4$

Step2: Rewrite the radical expression

$\sqrt[4]{3^4 x^4} = \sqrt[4]{(3x)^4}$

Step3: Simplify the 4th root

For even roots, $\sqrt[n]{a^n} = |a|$, so $\sqrt[4]{(3x)^4} = |3x| = 3|x|$

Answer:

$3|x|$