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Simplify. Express your answer using positive exponents. $\newline$ $\frac{8q^3}{2q}$

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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{8q^3}{2q}

Write Expression Groups: Write down the expression and group the coefficients and powers that have the same base. $\newline$ The expression is $\frac{8q^3}{2q}$ . We can group the coefficients ( $8$ and $2$ ) and the powers of $q$ ( $q^3$ and $q$ ).
Simplify Coefficients: Simplify the coefficients by dividing $8$ by $2$ . $8$ divided by $2$ equals $4$ . So, $\frac{8q^3}{2q}$ becomes $\frac{4q^3}{q}$ .
Simplify Powers: Simplify the powers of $q$ by subtracting the exponents. $\newline$ When dividing powers with the same base, subtract the exponents: $\frac{q^3}{q^1} = q^{3-1} = q^2$ .
Combine Results: Combine the results from Step $2$ and Step $3$ . $\newline$ We found that $8/2 = 4$ and $q^3/q = q^2$ . $\newline$ So, $8q^3/2q$ simplifies to $4q^2$ .

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