Question

How do you multiply and simplify `\frac { s t u ^ { 0} v } { s ^ { 2} t ^ { 3} u v ^ { 0} \cdot s ^ { 0} t ^ { 0} u v ^ { 0} }`?

Answer 1

See a solution process below:

Explanation:

First, use this rule of exponents to eliminate many of the terms and simplify the expression:

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

`(stu^color(red)(0)v)/(s^2t^3uv^color(red)(0) * s^color(red)(0)t^color(red)(0)uv^color(red)(0)) =>`

`(st * 1 * v)/(s^2t^3u * 1 * 1 * 1 * u * 1) =>`

`(stv)/(s^2t^3u * u)`

Next, use these rules of exponents to multiply the `u` terms and rewrite the numerator:

`a = a^color(red)(1)` and `x^color(red)(a) xx x^color(blue)(b) = x^(color(red)(a) + color(blue)(b))`

`(stv)/(s^2t^3u * u) =>`

`(stv)/(s^2t^3u^color(red)(1) * u^color(blue)(1)) =>`

`(stv)/(s^2t^3u^(color(red)(1)+color(blue)(1))) =>`

`(stv)/(s^2t^3u^2) =>`

`(s^color(red)(1)t^color(red)(1)v)/(s^2t^3u^2)`

Next, use these rules of exponents to complete the simplification:

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

`(s^color(red)(1)t^color(red)(1)v)/(s^color(blue)(2)t^color(blue)(3)u^2) =>`

`v/(s^(color(blue)(2)-color(red)(1))t^(color(blue)(3)-color(red)(1))u^2) =>`

`v/(s^color(red)(1)t^2u^2) =>`

`v/(st^2u^2)`