How do you simplify #(p^4 q^1.5)/(p^3 q-1/4)#?

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Answer 1 · 2017-10-31T10:30:17

See answer and processes below;

#(p^4 q^1.5)/(p^3 q^(-1/4))#

Please note that #q^1.5 = q^(cancel15/cancel10) = q^(5^3/5^2) = q^(3/2)#

Hence we have;

#(p^4 q^(3/2))/(p^3 q^(-1/4))#

Using indices to deduce..

#(p^4 q^(3/2)) div (p^3 q^(-1/4))#

Recall, #a^x div a^y = a^(x - y)#

#p^(4 - 3) xx q^(3/2 + 1/4), ( - xx - = +)#

#p^1 xx q^((6 + 1)/4)#

#p^1 xx q^(7/4)#

#p q^(7/4)#