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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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