which expression is equivalent to $(4h^7k^2)^4$?

* $16h^{11}k^6$
* $16h^{28}k^8$
* $256h^{11}k^6$
* $256h^{28}k^8$

Question

which expression is equivalent to $(4h^7k^2)^4$?

* $16h^{11}k^6$
* $16h^{28}k^8$
* $256h^{11}k^6$
* $256h^{28}k^8$

Accepted Answer

{ "quality": "clear", "question_count": 1, "skills_matched": [ "step_cot", "multiple_choice_formatter", "explain_then_answer", "tutor", "mastery_adaptive_brevity" ], "needs_drawing": false, "concepts_used": [ "Exponent Rules", "Power of a Product Rule" ], "new_concepts": [], "current_concepts": [ "Exponent Rules", "Power of a Product Rule" ] } ## Apply the power of a product rule Using the *Power of a Product Rule* and *Exponent Rules* knowledge points $$ (4h^7k^2)^4 = 4^4 \cdot (h^7)^4 \cdot (k^2)^4 $$ ## Simplify each factor Using the *Exponent Rules* knowledge point $$ \begin{aligned} 4^4 &= 256 \ (h^7)^4 &= h^{7 \cdot 4} = h^{28} \ (k^2)^4 &= k^{2 \cdot 4} = k^8 \end{aligned} $$ ## Combine the simplified terms Using the *Exponent Rules* knowledge point $$ 256h^{28}k^8 $$

(A) $16h^{11}k^6$

(B) $16h^{28}k^8$

(C) $256h^{11}k^6$

(D) $256h^{28}k^8$

{ "subject": "Mathematics", "question_type": "Multiple Choice", "knowledge_point": [ "Mathematics", "Algebra", "Exponent Rules" ] }

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QUESTION IMAGE

Question

Explanation:

Apply the power of a product rule

Simplify each factor

Combine the simplified terms

Answer: