find the values for $a$, $b$, and $c$ that complete the simplification.

\\sqrt{x^{12} y^9 z^5} = \sqrt{x^{12} \cdot y^8 \cdot y \cdot z^4 \cdot z} = x^a y^b z^c \sqrt{yz}\

$a = $

$b = $

$c = $

Question

find the values for $a$, $b$, and $c$ that complete the simplification.

\\sqrt{x^{12} y^9 z^5} = \sqrt{x^{12} \cdot y^8 \cdot y \cdot z^4 \cdot z} = x^a y^b z^c \sqrt{yz}\

$a = $

$b = $

$c = $

Accepted Answer

{ "quality": "clear", "question_count": 1, "skills_matched": [ "step_cot", "explain_then_answer", "tutor", "mastery_adaptive_brevity" ], "needs_drawing": false, "concepts_used": [ "Radical Simplification" ], "new_concepts": [], "current_concepts": [ "Radical Simplification", "Exponent Rules" ] } ## Simplify the radical expression Using the *Radical Simplification* knowledge point $$ \begin{aligned} \sqrt{x^{12} y^9 z^5} &= \sqrt{x^{12} \cdot y^8 \cdot y \cdot z^4 \cdot z} \ &= \sqrt{x^{12}} \cdot \sqrt{y^8} \cdot \sqrt{z^4} \cdot \sqrt{yz} \ &= x^6 y^4 z^2 \sqrt{yz} \end{aligned} $$ ## Identify the values of a, b, and c By comparing the simplified expression $x^6 y^4 z^2 \sqrt{yz}$ to the given form $x^a y^b z^c \sqrt{yz}$, we match the exponents: - $a = 6$ - $b = 4$ - $c = 2$ ## Question 1 Find the values for $a$, $b$, and $c$ that complete the simplification. $\sqrt{x^{12}y^9z^5} = \sqrt{x^{12} \cdot y^8 \cdot y \cdot z^4 \cdot z} = x^a y^b z^c \sqrt{yz}$ $a =$ 6 $b =$ 4 $c =$ 2 { "subject": "Mathematics", "question_type": "Fill-in-the-blank", "knowledge_point": [ "Mathematics", "Algebra", "Radical Simplification" ] }

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QUESTION IMAGE

Question

Explanation:

Simplify the radical expression

Identify the values of a, b, and c

Answer:

Question 1