fill-in-the-blank

suppose \frac{(a^8)^2 \cdot a^5}{(a^5)^2} = a^x, x =

Question

fill-in-the-blank

suppose \frac{(a^8)^2 \cdot a^5}{(a^5)^2} = a^x, x =

Accepted Answer

{ "quality": "clear", "question_count": 1, "skills_matched": [ "step_cot", "blank_filling_formatter", "explain_then_answer", "quick" ], "needs_drawing": false, "concepts_used": [], "new_concepts": [ "Exponent Rules", "Power of a Power Rule", "Quotient of Powers Rule" ], "current_concepts": [ "Exponent Rules", "Power of a Power Rule", "Quotient of Powers Rule" ] } ## Simplify the numerator and denominator using the power of a power rule $$ \begin{aligned} (a^8)^2 &= a^{8 \cdot 2} = a^{16} \ (a^5)^2 &= a^{5 \cdot 2} = a^{10} \end{aligned} $$ ## Simplify the numerator using the product of powers rule $$ (a^8)^2 \cdot a^5 = a^{16} \cdot a^5 = a^{16 + 5} = a^{21} $$ ## Simplify the entire fraction using the quotient of powers rule $$ \frac{a^{21}}{a^{10}} = a^{21 - 10} = a^{11} \implies x = 11 $$ Suppose $\frac{(a^8)^2 \cdot a^5}{(a^5)^2} = a^x$, $x =$ 11. { "subject": "Mathematics", "question_type": "Fill-in-the-blank", "knowledge_point": [ "Mathematics", "Algebra", "Exponent Rules" ] }

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Question

Explanation:

Simplify the numerator and denominator using the power of a power rule

Simplify the numerator using the product of powers rule

Simplify the entire fraction using the quotient of powers rule

Answer: