Question

simplify the radical expression. $sqrt{x^{19}}$ write your answer in the form a, $sqrt{b}$, or $asqrt{b}$, constants or expressions in x. use at most one radical at most one absolute value symbol in your expression

Explanation:

Step1: Split exponent into even + odd

$\sqrt{x^{19}} = \sqrt{x^{18} \cdot x}$

Step2: Separate radicals

$\sqrt{x^{18} \cdot x} = \sqrt{x^{18}} \cdot \sqrt{x}$

Step3: Simplify $\sqrt{x^{18}}$

$\sqrt{x^{18}} = |x^9|$

Step4: Combine terms

$|x^9| \cdot \sqrt{x} = |x|^9\sqrt{x}$

Answer:

$|x|^9\sqrt{x}$