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Simplify. Express your answer using positive exponents. $\newline$ $\frac{6u^3}{2u^9}$

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Simplify exponential expressions using the multiplication rule

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Q. Simplify. Express your answer using positive exponents.

\newline

\frac{6u^3}{2u^9}

Write Expression: Write down the given expression. $\newline$ We have the expression $\frac{6u^3}{2u^9}$ .
Simplify Coefficients: Simplify the coefficients (numbers in front of the variables). $\newline$ Divide $6$ by $2$ to simplify the coefficients. $\newline$ $6 / 2 = 3$
Apply Quotient Rule: Apply the quotient rule for exponents. $\newline$ When dividing powers with the same base, subtract the exponents. $\newline$ $u^3 / u^9 = u^{(3-9)} = u^{-6}$
Express with Positive Exponent: Express the answer with a positive exponent. $\newline$ Since we want to express the answer with positive exponents, we rewrite $u^{-6}$ as $1/u^6$ .
Combine Results: Combine the results from Step $2$ and Step $4$ . $\newline$ The simplified expression is $3 \times \frac{1}{u^6}$ , which can be written as $\frac{3}{u^6}$ .

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