How do you simplify \frac { 3p ^ { 9} q ^ { 3} } { 4} \times \frac { p } { 6q ^ { 3} }3p9q34×p6q3?

2 Answers
Nov 25, 2017

p^10/8p108

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)3p9q34p6q3

Cross out the common q^3 q3 on both sides
(3p^9)/4 * p/(6)3p94p6

Cross out the common 3 on both sides
(p^9)/4 * p/2 p94p2

Multiply
p^10 / 8p108

Nov 25, 2017

(p^10 ) / (8)p108

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)3p9q3p46q3

in the denominator 4 * 6 = 24 so : (3p^9q^3 * p) / (24q^3)3p9q3p24q3

in the nominator we have a pp and a p^9p9 so we multiply those two, or rather add their powers, (remember p = p^1p=p1, so p^9*p = p^10p9p=p10)
so (3p^10q^3 ) / (24q^3)3p10q324q3

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

we get rid of q^3q3 so (3p^10 ) / (24)3p1024

note that 24 = 3 * 824=38 so we can get rid of the 33
(3p^10 ) / (24)3p1024= (3p^10 ) / (3 * 8)3p1038

therefore

(p^10 ) / (8)p108