which expression shows the simplified form of $(8r^{-5})^{-3}$?

* $8r^{15}$
* $\frac{8}{r^{15}}$
* $512r^{15}$
* $\frac{r^{15}}{512}$

Question

which expression shows the simplified form of $(8r^{-5})^{-3}$?

* $8r^{15}$
* $\frac{8}{r^{15}}$
* $512r^{15}$
* $\frac{r^{15}}{512}$

Accepted Answer

{ "quality": "clear", "question_count": 1, "skills_matched": [ "step_cot", "multiple_choice_formatter", "explain_then_answer", "quick" ], "needs_drawing": false, "concepts_used": [ "Exponent Rules", "Negative Exponents" ], "new_concepts": [], "current_concepts": [ "Exponent Rules", "Negative Exponents", "Power of a Product Rule" ] } ## Apply the power of a product rule $$ (8r^{-5})^{-3} = 8^{-3} \cdot (r^{-5})^{-3} $$ ## Simplify the exponents $$ \begin{aligned} 8^{-3} &= \frac{1}{8^3} = \frac{1}{512} \ (r^{-5})^{-3} &= r^{(-5) \cdot (-3)} = r^{15} \end{aligned} $$ ## Combine the terms $$ \frac{1}{512} \cdot r^{15} = \frac{r^{15}}{512} $$

(A) $8r^{15}$

(B) $\frac{8}{r^{15}}$

(C) $512r^{15}$

(D) $\frac{r^{15}}{512}$

{ "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 the exponents

Combine the terms

Answer: