Reduce the fraction below to its simplest form. $\frac { 14 q ^ { 3 } n ^ { 9 } } { 21 n ^ { 2 } q ^ { 5 } }$
A) $\frac { 2 n } { 3 q ^ { 2 } }$
B) $\frac { 2 n ^ { 11 } } { 3 q ^ { 8 } }$
C) $\frac { 3 n } { 2 q ^ { 2 } }$
D) $\frac { 2 n ^ { 7 } } { 3 q ^ { 9 } }$

Question

Quizplus · Accepted Answer

To simplify the fraction, we can divide the numerator and denominator by the greatest common factor, which is 7n^2q^3. 
\begin{align*}
\frac{14q^3n^9}{21n^2q^5} &= \frac{2\cdot7\cdot q^3\cdot n^9}{3\cdot7\cdot n^2\cdot q^5}\
&= \frac{2}{3}\cdot\frac{n^9}{n^2}\cdot\frac{1}{q^2}\cdot\frac{1}{q^3}\
&= \frac{2n^7}{3q^5}\
&= \frac{2n}{3q^2}
\end{align*} 
Therefore, the answer is A.

Reduce the Fraction Below to Its Simplest Form 14q3n921n2q5\frac { 14 q ^ { 3 } n ^ { 9 } } { 21 n ^ { 2 } q ^ { 5 } }21n2q514q3n9​

Reduce the Fraction Below to Its Simplest Form $\frac { 14 q ^ { 3 } n ^ { 9 } } { 21 n ^ { 2 } q ^ { 5 } }$