How do you simplify #\frac { 15p ^ { 3} m ^ { 5} } { 24m ^ { 2} p ^ { 3} }#?

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Answer 1 · 2017-06-10T02:32:11

See a solution process below:

First, rewrite the expression as:

#15/24(m^5/m^2)(p^3/p^3) =>#

#15/24(m^5/m^2)(color(red)(cancel(color(black)(p^3)))/color(red)(cancel(color(black)(p^3)))) =>#

#((3 xx 5)/(3 xx 8))(m^5/m^2) =>#

#((color(red)(cancel(color(black)(3))) xx 5)/(color(red)(cancel(color(black)(3))) xx 8))(m^5/m^2) =>#

#5/8(m^5/m^2)#

Now, use this rule of exponents to simplify the #m# term:

#x^color(red)(a)/x^color(blue)(b) = x^(color(red)(a)-color(blue)(b))#

#5/8(m^color(red)(5)/m^color(blue)(2)) =>#

#5/8(m^(color(red)(5)-color(blue)(2))) =>#

#5/8(m^3) =>#

#(5m^3)/8#