Full solution

Q. Simplify. Express your answer using positive exponents.

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\frac{9y^2}{(3y)(y^5)}

Simplify Coefficients: Simplify the coefficients (numerical parts) of the expression. $\newline$ We have the coefficient $9$ in the numerator and $3$ in the denominator. We divide $9$ by $3$ to simplify. $\newline$ $9 / 3 = 3$
Apply Quotient Rule: Apply the quotient rule for the $y$ terms. $\newline$ The quotient rule of exponents states that when we divide powers with the same base, we subtract the exponents. $\newline$ $\frac{y^2}{y^1} = y^{(2-1)} = y^1$
Simplify Y Terms: Simplify the remaining y terms. $\newline$ We have $y^1$ in the numerator and $y^5$ in the denominator. We apply the quotient rule again. $\newline$ $y^1 / y^5 = y^{(1-5)} = y^{-4}$
Combine Results: Combine the results from Step $1$ and Step $3$ . $\newline$ We multiply the simplified coefficient from Step $1$ with the simplified $y$ term from Step $3$ . $\newline$ $3 \times y^{-4}$
Express with Positive Exponents: Express the answer using positive exponents. $\newline$ Since we have a negative exponent, we can rewrite $y^{-4}$ as $1/y^4$ to express it with a positive exponent. $\newline$ $3 \times (1/y^4) = 3/y^4$