First, rewrite the expression as:
#(6/4)(r^2/r)(p^3/p^4) =>#
#((3 xx 2)/(2 xx 2))(r^2/r)(p^3/p^4) =>#
#((3 xx color(red)(cancel(color(black)(2))))/(2 xx color(red)(cancel(color(black)(2)))))(r^2/r)(p^3/p^4) =>#
#3/2(r^2/r)(p^3/p^4)#
Next, use these rules of exponents to simplify the #r# terms:
#a = a^color(blue)(1)# and #x^color(red)(a)/x^color(blue)(b) = x^(color(red)(a)-color(blue)(b))# and #a^color(red)(1) = a#
#3/2(r^color(red)(2)/r^color(blue)(1))(p^3/p^4) => #
#3/2(r^(color(red)(2)-color(blue)(1)))(p^3/p^4) => #
#3/2(r^1)(p^3/p^4) => #
#3/2(r)(p^3/p^4) => #
#(3r)/2(p^3/p^4)#
Now, use these rules of exponents to simplify the #p# terms:
#x^color(red)(a)/x^color(blue)(b) = 1/x^(color(blue)(b)-color(red)(a))# and #a^color(red)(1) = a#
#(3r)/2(p^color(red)(3)/p^color(blue)(4)) =>#
#(3r)/2(1/p^(color(blue)(4)-color(red)(3))) =>#
#(3r)/2(1/p^1) =>#
#(3r)/2(1/p) =>#
#(3r)/(2p)#
From the original expression, because we cannot divide by #0#:
#4rp^4 != 0#
Or
#r != 0# and #p != 0#
