Question

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

Answer 1

`p^10/8`

Explanation:

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

`(3p^9q^3)/4 * p/(6q^3)`

Cross out the common `q^3` on both sides
`(3p^9)/4 * p/(6)`

Cross out the common 3 on both sides
`(p^9)/4 * p/2`

Multiply
`p^10 / 8`

Answer 2

`(p^10 ) / (8)`

Explanation:

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

(the dot `*` 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)

`(3p^9q^3 * p) / (4 * 6q^3)`

in the denominator 4 * 6 = 24 so : `(3p^9q^3 * p) / (24q^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*p = p^10`)
so `(3p^10q^3 ) / (24q^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 `(3p^10 ) / (24)`

note that `24 = 3 * 8` so we can get rid of the `3`
`(3p^10 ) / (24)`= `(3p^10 ) / (3 * 8)`

therefore

`(p^10 ) / (8)`