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Simplify. Express your answer using positive exponents. $\newline$ $\frac{10k}{2k^9}$

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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{10k}{2k^9}

Write Expression and Identify Terms: Write down the expression and identify like terms. $\newline$ The expression is $\frac{10k}{2k^9}$ . We can simplify this by dividing the coefficients ( $10$ and $2$ ) and subtracting the exponents of like bases ( $k$ and $k^9$ ).
Divide Coefficients: Divide the coefficients. $10$ divided by $2$ equals $5$ .
Apply Quotient Rule for Exponents: Apply the quotient rule for exponents. The quotient rule states that when dividing like bases, you subtract the exponents: $\frac{k}{k^9} = k^{1-9} = k^{-8}.$
Combine Results: Combine the results of steps $2$ and $3$ . $\newline$ We have the coefficient $5$ from step $2$ and the exponent $k^{-8}$ from step $3$ . Combining these gives us $5k^{-8}$ .
Express with Positive Exponents: Express the answer with positive exponents. $\newline$ Since $k^{-8}$ is the same as $1/k^8$ , we can rewrite $5k^{-8}$ as $5/k^8$ .

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