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

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Simplify exponential expressions using the multiplication and division rules

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Q. Simplify. Express your answer using positive exponents.

\newline

\frac{9a^6}{a^3 \cdot 3a}

Write Expression and Group: Write down the expression and group the coefficients and powers that have the same base. $\newline$ The expression is $\frac{9a^6}{a^3 \cdot 3a}$ . We can group the coefficients $(9$ and $3)$ and the powers of $a$ ( $a^6$ , $a^3$ , and $a$ ).
Simplify Coefficients: Simplify the coefficients. $\newline$ The coefficient $9$ can be divided by $3$ , which is part of the denominator. $\newline$ $\frac{9}{3} = 3$
Apply Quotient Rule: Apply the quotient rule for exponents. $\newline$ When we divide powers with the same base, we subtract the exponents. $\newline$ $a^6 / (a^3 \cdot a)$ can be simplified by subtracting the exponents in the denominator from the exponent in the numerator. $\newline$ $a^6 / a^{3+1} = a^6 / a^4 = a^{6-4} = a^2$
Combine Results: Combine the results from Step $2$ and Step $3$ . $\newline$ We found: $\newline$ $\frac{9}{3} = 3$ $\newline$ $\frac{a^6}{a^4} = a^2$ $\newline$ Now, we combine these results to write the expression in simplest form. $\newline$ $\frac{9a^6}{a^3 \times 3a} = 3 \times a^2$

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