mr. walden wrote the expression $\frac{p^{-5}}{q^0}$. he asked his students to write an equivalent expression of $\frac{p^{-5}}{q^0}$.

four students wrote these expressions.

isaac: $\frac{q^0}{p^5}$
rosa: $p^{-5} + q^0$
bruce: $p^5 q^0$
brianna: $\frac{1}{p^5 q^0}$

which student wrote the correct equation that can be simplified to be equivalent to mr. waldens equation?

isaac
rosa
bruce
brianna

Question

mr. walden wrote the expression $\frac{p^{-5}}{q^0}$. he asked his students to write an equivalent expression of $\frac{p^{-5}}{q^0}$.

four students wrote these expressions.

isaac: $\frac{q^0}{p^5}$
rosa: $p^{-5} + q^0$
bruce: $p^5 q^0$
brianna: $\frac{1}{p^5 q^0}$

which student wrote the correct equation that can be simplified to be equivalent to mr. waldens equation?

isaac
rosa
bruce
brianna

Accepted Answer

{ "quality": "clear", "question_count": 1, "skills_matched": [ "step_cot", "multiple_choice_formatter", "explain_then_answer", "quick" ], "needs_drawing": false, "concepts_used": [], "new_concepts": [ "Exponent Rules", "Negative Exponents" ], "current_concepts": [ "Exponent Rules", "Negative Exponents" ] } ## Simplify the original expression $$ \frac{p^{-5}}{q^0} = \frac{p^{-5}}{1} = p^{-5} = \frac{1}{p^5} $$ ## Evaluate each student's expression $$ \begin{aligned} &\text{Isaac: } \frac{p^5}{q^0} = \frac{p^5}{1} = p^5 \ &\text{Rosa: } p^{-5} + q^0 = p^{-5} + 1 \ &\text{Bruce: } p^5 q^0 = p^5 \cdot 1 = p^5 \ &\text{Brianna: } \frac{1}{p^5 q^0} = \frac{1}{p^5 \cdot 1} = \frac{1}{p^5} \end{aligned} $$ ## Identify the matching student $$ \text{Brianna's expression simplifies to } \frac{1}{p^5} \text{, which is equivalent to } \frac{p^{-5}}{q^0}. $$

Isaac

Rosa

Bruce

Brianna

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

Sovi.AI - AI Math Tutor

QUESTION IMAGE

Question

Explanation:

Simplify the original expression

Evaluate each student's expression

Identify the matching student

Answer: