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$Question 5 (4 points) "The Snow-Shoveling Swoosher" Simplify. Negative exponents can stay above the fraction bar. If variables cancel, enter a "0", (6a^(-4)bc^(-4))(3a^(2)b^(6)c)(9a^(7)b^(-5)c^(-4))= qquad a qquad b c qquad Blank 1: ◻ Blank 2: ◻ Blank 3: ◻ Blank 4: ◻$

Question $5$ ( $4$ points) $\newline$

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Simplify exponential expressions using the multiplication and division rules

Full solution

Q. Question

5

(

4

points)

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Question Prompt: Question prompt: Simplify the expression $(6a^{-4}bc^{-4})(3a^{2}b^{6}c)(9a^{7}b^{-5}c^{-4})$ .
Combine Coefficients: Combine the coefficients $6, 3,$ and $9$ by multiplying them together. $6 \times 3 \times 9 = 18 \times 9 = 162.$
Add Exponents for $a$ : Add the exponents for the variable $a$ . Remember that when you multiply with the same base, you add the exponents: $a^{-4} \times a^{2} \times a^{7} = a^{-4 + 2 + 7} = a^{5}$ .
Add Exponents for $b$ : Add the exponents for the variable $b$ . Do the same as with $a$ : $b \times b^{6} \times b^{-5} = b^{1 + 6 - 5} = b^{2}$ .
Add Exponents for $c$ : Add the exponents for the variable $c$ . Again, add the exponents: $c^{(-4)} \cdot c \cdot c^{(-4)} = c^{(-4 + 1 - 4)} = c^{(-7)}$ .
Combine All Parts: Combine all the parts to write the simplified expression. $\newline$ The final expression is $162a^{5}b^{2}c^{-7}$ .

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