use the product rule to simplify the expression. write the result using exponents.

$(b^7c)(b^{10}c^7)$

$(b^7c)(b^{10}c^7) = $

Question

use the product rule to simplify the expression. write the result using exponents.

$(b^7c)(b^{10}c^7)$

$(b^7c)(b^{10}c^7) = $

Accepted Answer

{ "quality": "clear", "question_count": 1, "skills_matched": [ "step_cot", "blank_filling_formatter", "explain_then_answer", "quick" ], "needs_drawing": false, "concepts_used": [ "Product Rule for Exponents", "Multiplying Monomials" ], "new_concepts": [], "current_concepts": [ "Product Rule for Exponents", "Multiplying Monomials" ] } ## Group like bases together $$ (b^7c)(b^{10}c^7) = (b^7 \cdot b^{10})(c^1 \cdot c^7) $$ ## Apply the product rule for exponents $$ \begin{aligned} b^7 \cdot b^{10} &= b^{7+10} = b^{17} \ c^1 \cdot c^7 &= c^{1+7} = c^8 \end{aligned} $$ ## Combine the simplified terms $$ (b^7c)(b^{10}c^7) = b^{17}c^8 $$ Use the product rule to simplify the expression. Write the result using exponents. $(b^7c)(b^{10}c^7) =$ $b^{17}c^8$ { "subject": "Mathematics", "question_type": "Fill-in-the-blank", "knowledge_point": [ "Mathematics", "Algebra", "Product Rule for Exponents" ] }

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QUESTION IMAGE

Question

Explanation:

Group like bases together

Apply the product rule for exponents

Combine the simplified terms

Answer: