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Simplify. Express your answer using positive exponents. $\newline$ $(5u^3)(9u^2)$

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Simplify exponential expressions using the multiplication rule

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Q. Simplify. Express your answer using positive exponents.

\newline

(5u^3)(9u^2)

Identify Components: Identify the components of the expression that can be combined. $\newline$ We have two terms, $5u^3$ and $9u^2$ , which can be multiplied together. We will group the coefficients ( $5$ and $9$ ) and the powers of $u$ ( $u^3$ and $u^2$ ) separately.
Multiply Coefficients: Multiply the coefficients. $\newline$ Calculate the product of the coefficients $5$ and $9$ . $\newline$ $5 \times 9 = 45$
Combine Powers: Combine the powers of $u$ . $\newline$ When multiplying powers with the same base, we add the exponents. $\newline$ $u^3 \times u^2 = u^{(3+2)} = u^5$
Write Expression: Write the simplified expression. $\newline$ Combine the results from Step $2$ and Step $3$ to get the final simplified expression. $\newline$ $(5u^3)(9u^2) = 45u^5$

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