Question

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

Explanation:

Step1: Factor the constant

$\sqrt[4]{256x^7} = \sqrt[4]{256 \cdot x^7}$

Step2: Simplify 4th root of 256

$\sqrt[4]{256} = 4$, so we get $4\sqrt[4]{x^7}$

Step3: Split $x^7$ into perfect 4th power

$x^7 = x^4 \cdot x^3$, so $4\sqrt[4]{x^4 \cdot x^3}$

Step4: Separate the radicals

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

Step5: Simplify $\sqrt[4]{x^4}$

$\sqrt[4]{x^4} = |x|$, so final expression is $4|x|\sqrt[4]{x^3}$

Answer:

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