How do you simplify #(6r^2p^3)/(4rp^4)# and find any non permissible values?

Question

Nathan Axel · Accepted Answer

See a solution process below:

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#

Avery Alexander · Answer

undefined To simplify (6r^2p^3)/(4rp^4), we can divide the coefficients and subtract the exponents of the variables.

The simplified form is (3/2)(r^2)/(p).

The non-permissible values are those that make the denominator equal to zero. In this case, p cannot be equal to zero.