How do you simplify #(3stuv)/{ 3s ^ { 5} t ^ { 7} u v ^ { 3} \cdot s ^ { 6} t u v ^ { 6} }#?

1 Answer
smendyka
Feb 1, 2018

See a solution process below:

Explanation:

First, rewrite the expression as:

#(3/3)(s/(s^5 * s^6))(t/(t^7 * t))(u/(u * u))(v/(v^3 * v^6)) =>#

#1(s/(s^5 * s^6))(color(red)(cancel(color(black)(t)))/(t^7 * color(red)(cancel(color(black)(t)))))(color(red)(cancel(color(black)(u)))/(color(red)(cancel(color(black)(u))) * u))(v/(v^3 * v^6)) =>#

#(s/(s^5 * s^6))(1/t^7)(1/u)(v/(v^3 * v^6))#

Next, use this rule of exponents to rewrite the expression again:

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

#(s^1/(s^5 * s^6))(1/t^7)(1/u)(v^1/(v^3 * v^6))#

Then, use this rule of exponents to simplify the denominators:

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

#(s^1/(s^color(red)(5) * s^color(blue)(6)))(1/t^7)(1/u)(v^1/(v^color(red)(3) * v^color(blue)(6))) =>#

#(s^1/s^(color(red)(5)+color(blue)(6)))(1/t^7)(1/u)(v^1/v^(color(red)(3)+color(blue)(6))) =>#

#(s^1/s^11)(1/t^7)(1/u)(v^1/v^9)#

Now, use this rule of exponents to complete the simplification:

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

#(s^color(red)(1)/s^color(blue)(11))(1/t^7)(1/u)(v^color(red)(1)/v^color(blue)(9)) =>#

#(1/s^(color(blue)(11)-color(red)(1)))(1/t^7)(1/u)(1/v^(color(blue)(9)-color(red)(1))) =>#

#(1/s^10)(1/t^7)(1/u)(1/v^8) =>#

#1/(s^10t^7uv^8)#

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