Question

simplify the radical expression.
\\(\sqrt3{-x^{18}}\\)
write your answer in the form \\(a\\), \\(\sqrt3{b}\\), or \\(a\sqrt3{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: Rewrite negative term

$\sqrt[3]{-x^{18}} = \sqrt[3]{-1 \cdot x^{18}}$

Step2: Split the cube root

$\sqrt[3]{-1} \cdot \sqrt[3]{x^{18}}$

Step3: Evaluate roots

$\sqrt[3]{-1} = -1$, $\sqrt[3]{x^{18}} = x^{6}$ (since $18 \div 3 = 6$)

Step4: Multiply results

$-1 \cdot x^{6} = -x^6$

Answer:

$-x^6$