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Simplify. Express your answer using positive exponents. $\newline$ $(2v^3)(4v)(5v)$ $\newline$ ______

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Simplify exponential expressions using the multiplication and division rules

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Q. Simplify. Express your answer using positive exponents.

\newline

(2v^3)(4v)(5v)

\newline

______

Grouping coefficients and variables: Group the coefficients and the variables with the same base. $\newline$ We have the expression $(2v^3)(4v)(5v)$ . We can group the coefficients $(2, 4, 5)$ and the variables with the same base $(v^3, v, v)$ together.
Multiplying the coefficients: Multiply the coefficients. $\newline$ Now we multiply the coefficients $2$ , $4$ , and $5$ together. $\newline$ $2 \times 4 \times 5 = 8 \times 5 = 40$
Applying the product rule for exponents: Apply the product rule for exponents. $\newline$ When multiplying powers with the same base, we add the exponents. We have $v^3$ , $v$ , and $v$ which is equivalent to $v^1$ and $v^1$ . So we add the exponents $3$ , $1$ , and $1$ . $\newline$ $v^3 \cdot v^1 \cdot v^1 = v^{(3+1+1)} = v^5$
Combining the results: Combine the results from Step $2$ and Step $3$ . $\newline$ We have found that the product of the coefficients is $40$ and the product of the variables is $v^5$ . Now we combine them to get the final simplified expression. $\newline$ $40 \times v^5 = 40v^5$

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Which expression is equivalent to

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\newline

\newline

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Question

A baker has three banana muffin recipes. Recipe A uses

3

bananas to make

12

muffins. Recipe B uses

5

bananas to make

24

muffins. Recipe C uses

11

bananas to make

48

muffins. Rutendo tried to order the recipes from least to greatest by bananas per muffin, but he made a mistake. Here's his work:

\newline

\frac{12}{3} = 4

\newline

\frac{24}{5} = 4.8

\newline

\frac{48}{11} \approx 4.36

\newline

4

<

4.36

<

4.8

\newline

What was Rutendo's mistake? Choose

1

\newline

(Choice A) Rutendo calculated muffins per banana instead of bananas per muffin.

\newline

(Choice B) The number

4.36

is greater than

4.8

\newline

(Choice C) Rutendo ordered by number of muffins instead of by bananas per muffin.

Posted 3 hours ago

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