Question

use the product rule to simplify the following expression. assume that variables represent nonnegative real numbers.
\\(sqrt{x^{5}}\\)
\\(sqrt{x^{5}} = square\\) (type an exact answer, using radicals as needed.)

Explanation:

Step1: Split exponent into sum

$x^5 = x^{4+1} = x^4 \cdot x^1$

Step2: Apply square root product rule

$\sqrt{x^5} = \sqrt{x^4 \cdot x} = \sqrt{x^4} \cdot \sqrt{x}$

Step3: Simplify perfect square root

$\sqrt{x^4} = x^2$

Step4: Combine terms

$\sqrt{x^5} = x^2\sqrt{x}$

Answer:

$x^2\sqrt{x}$