Question

simplify the radical expression. $sqrt4{256x^{7}}$ write your answer in the form a, $sqrt4{b}$, or $asqrt4{b}$, where a and b are constants or expressions in x. use at most one radical in your answer, at most one absolute value symbol in your expression for a.

Explanation:

Step1: Factor the constant term

$256 = 4^4$

Step2: Rewrite the variable exponent

$x^7 = x^{4+3} = x^4 \cdot x^3$

Step3: Split the 4th root

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

Step4: Simplify the perfect 4th root

$\sqrt[4]{4^4 x^4} = 4|x|$

Step5: Combine terms

$4|x| \cdot \sqrt[4]{x^3}$

Answer:

$4|x|\sqrt[4]{x^3}$