# How do you simplify \frac { 3p ^ { 9} q ^ { 3} } { 4} \times \frac { p } { 6q ^ { 3} }?

Nov 25, 2017

${p}^{10} / 8$

#### Explanation:

Cross out the like terms of both sides; cross out what’s common between the two fractions

$\frac{3 {p}^{9} {q}^{3}}{4} \cdot \frac{p}{6 {q}^{3}}$

Cross out the common ${q}^{3}$ on both sides
$\frac{3 {p}^{9}}{4} \cdot \frac{p}{6}$

Cross out the common 3 on both sides
$\frac{{p}^{9}}{4} \cdot \frac{p}{2}$

Multiply
${p}^{10} / 8$

Nov 25, 2017

$\frac{{p}^{10}}{8}$

#### Explanation:

put all under same fraction since there is only terms to multiply,

(the dot $\cdot$ is the same as x, the times symbol, we don't really need to write it, but I kept it for you to see the two terms)

$\frac{3 {p}^{9} {q}^{3} \cdot p}{4 \cdot 6 {q}^{3}}$

in the denominator 4 * 6 = 24 so : $\frac{3 {p}^{9} {q}^{3} \cdot p}{24 {q}^{3}}$

in the nominator we have a $p$ and a ${p}^{9}$ so we multiply those two, or rather add their powers, (remember $p = {p}^{1}$, so ${p}^{9} \cdot p = {p}^{10}$)
so $\frac{3 {p}^{10} {q}^{3}}{24 {q}^{3}}$

now we start to get rid of same terms and factors found both in the denominator and nominator

we get rid of ${q}^{3}$ so $\frac{3 {p}^{10}}{24}$

note that $24 = 3 \cdot 8$ so we can get rid of the $3$
$\frac{3 {p}^{10}}{24}$= $\frac{3 {p}^{10}}{3 \cdot 8}$

therefore

$\frac{{p}^{10}}{8}$