How do you simplify #(20qr^-2t^-5)/(rq^0r^4t^-2)#?

1 Answer
May 15, 2017

Answer:

See a solution process below:

Explanation:

First, rewrite this expression as:

#20(q/q^0)(r^-2/(r * r^4))(t^-5/t^-2)#

Next, simplify the #q# term using this rule of exponents:

#a^color(red)(0) = 1#

#20(q/q^color(red)(0))(r^-2/(r * r^4))(t^-5/t^-2) => 20(q/color(red)(1))(r^-2/(r * r^4))(t^-5/t^-2) =>#

#20q(r^-2/(r * r^4))(t^-5/t^-2)#

Next, use these rules of exponents to simplify the #r# terms:

#a = a^color(red)(1)# and #x^color(red)(a) xx x^color(blue)(b) = x^(color(red)(a) + color(blue)(b))# and #x^color(red)(a)/x^color(blue)(b) = 1/x^(color(blue)(b)-color(red)(a))#

#20q(r^-2/(r * r^4))(t^-5/t^-2) => 20q(r^-2/(r^color(red)(1) * r^color(blue)(4)))(t^-5/t^-2) =>#

#20q(r^-2/(r^(color(red)(1) + color(blue)(4))))(t^-5/t^-2) => 20q(r^color(red)(-2)/(r^color(blue)(5)))(t^-5/t^-2) =>#

#20q(1/(r^(color(blue)(5) - color(red)(-2))))(t^-5/t^-2) => 20q(1/(r^(color(blue)(5) + color(red)(2))))(t^-5/t^-2) =>#

#20q(1/r^7)(t^-5/t^-2) => (20q)/r^7(t^-5/t^-2)#

Now, use this rule to simplify the #t# terms:

#x^color(red)(a)/x^color(blue)(b) = 1/x^(color(blue)(b)-color(red)(a))#

#(20q)/r^7(t^color(red)(-5)/t^color(blue)(-2)) => (20q)/r^7(1/t^(color(blue)(-2)-color(red)(-5))) => (20q)/r^7(1/t^(color(blue)(-2)+color(red)(5))) =>#

#(20q)/r^7(1/t^3) => (20q)/(r^7t^3)#