How do you simplify #((2r^3)/s)^2(s/r^3)^3# and write it using only positive exponents?

2 Answers
Feb 7, 2017

Answer:

#((2r^3)/s)^2(s/r^3)^3=(4s)/(r^3)#

Explanation:

#((2r^3)/s)^2(s/r^3)^3 = (2^2r^(3*2))/(s^2)*s^3/r^(3*3)#

#=(4r^6)/s^2*s^3/r^9#

#= (4s^(3-2))/(r^(9-6))#

#=(4s)/(r^3)#

Feb 7, 2017

Answer:

See the entire simplification process below:

Explanation:

First use these two rules for exponents to begin simplifying:

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

#(x^color(red)(a))^color(blue)(b) = x^(color(red)(a) xx color(blue)(b))#

#((2r^3)/s)^2(s/r^3)^3 -> ((2^color(red)(1)r^color(red)(3))/s^color(red)(1))^color(blue)(2)(s^color(red)(1)/r^color(red)(3))^color(blue)(3) ->#

#(2^(color(red)(1) xx color(blue)(2))r^(color(red)(3) xx color(blue)(2)))/s^(color(red)(1) xx color(blue)(2)) xx s^(color(red)(1) xx color(blue)(3)) /r^(color(red)(3) xx color(blue)(3)) -> (2^2r^6s^3)/(s^2r^9) -> (4r^6s^3)/(s^2r^9)#

Now, use these two rules for exponents to complete the simplification:

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

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

#(4r^color(red)(6)s^color(red)(3))/(s^color(blue)(2)r^color(blue)(9)) -> (4s^(color(red)(3)-color(blue)(2)))/r^(color(blue)(9)-color(red)(6)) -> (4s^1)/r^3 -> (4s)/r^3#