Question

14
enter the correct answer in the box.
if ( x > 0 ), what is the quotient of ( 20sqrt{x^6} div sqrt{16x^7} ) in simplest radical form? if necessary, rationalize the denominator.
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Explanation:

Step1: Rewrite division as fraction

$20\sqrt{x^6} \div \sqrt{16x^7} = \frac{20\sqrt{x^6}}{\sqrt{16x^7}}$

Step2: Simplify square roots

$\sqrt{x^6}=x^3$, $\sqrt{16x^7}=4x^3\sqrt{x}$
Substitute: $\frac{20x^3}{4x^3\sqrt{x}}$

Step3: Simplify coefficients and variables

Cancel $x^3$, divide $20/4=5$: $\frac{5}{\sqrt{x}}$

Step4: Rationalize the denominator

Multiply numerator/denominator by $\sqrt{x}$: $\frac{5\sqrt{x}}{\sqrt{x} \cdot \sqrt{x}} = \frac{5\sqrt{x}}{x}$

Answer:

$\frac{5\sqrt{x}}{x}$