enter the correct answer in the box.

if $z 0$, what is the quotient of $20\sqrt{z^6} \div \sqrt{16z^7}$ in simplest radical form? if necessary, rationalize the denominator.

Question

enter the correct answer in the box.

if $z > 0$, what is the quotient of $20\sqrt{z^6} \div \sqrt{16z^7}$ in simplest radical form? if necessary, rationalize the denominator.

Accepted Answer

{ "quality": "clear", "question_count": 1, "skills_matched": [ "step_cot", "blank_filling_formatter", "explain_then_answer", "quick" ], "needs_drawing": false, "concepts_used": [ "Radical Simplification", "Exponent Rules" ], "new_concepts": [], "current_concepts": [ "Radical Simplification", "Exponent Rules", "Rationalizing the Denominator" ] } ## Simplify the individual radical expressions $$ \begin{aligned} 20\sqrt{z^6} &= 20z^3 \quad (\text{since } z > 0) \ \sqrt{16z^7} &= 4z^3\sqrt{z} \end{aligned} $$ ## Set up the quotient and simplify $$ \begin{aligned} \frac{20\sqrt{z^6}}{\sqrt{16z^7}} &= \frac{20z^3}{4z^3\sqrt{z}} \ &= \frac{5}{\sqrt{z}} \end{aligned} $$ ## Rationalize the denominator $$ \begin{aligned} \frac{5}{\sqrt{z}} \cdot \frac{\sqrt{z}}{\sqrt{z}} &= \frac{5\sqrt{z}}{z} \end{aligned} $$ If $z > 0$, what is the quotient of $20\sqrt{z^6} \div \sqrt{16z^7}$ in simplest radical form? If necessary, rationalize the denominator. $\frac{5\sqrt{z}}{z}$ { "subject": "Mathematics", "question_type": "Fill-in-the-blank", "knowledge_point": [ "Mathematics", "Algebra", "Radical Simplification" ] }

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QUESTION IMAGE

Question

Explanation:

Simplify the individual radical expressions

Set up the quotient and simplify

Rationalize the denominator

Answer: