Question

How do you simplify `\frac { u v ^ { 0} } { 2u ^ { 4} v ^ { - 4} }`?

Answer 1

See a solution process below:

Explanation:

First, rewrite the expression as:

`1/2(u/u^4)(v^0/v^-4)`

Next, use these rules of exponents to simplify the `u` term:

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

`1/2(u/u^4)(v^0/v^-4) = (1/2)(u^color(red)(1)/u^color(blue)(4))(v^0/v^-4) =`

`1/2(1/u^(color(blue)(4)-color(red)(1)))(v^0/v^-4) = (1/2)(1/u^3)(v^0/v^-4) =`

`1/(2u^3)(v^0/v^-4)`

To begin the simplification of the `v` term use this rule of exponents:

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

`1/(2u^3)(v^color(red)(0)/v^-4) = 1/(2u^3)(1/v^-4)`

Now, use this rule of exponents to eliminate the negative exponent:

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

`1/(2u^3)(1/v^color(red)(-4)) = 1/(2u^3)(v^color(red)(- -4)) = 1/(2u^3)(v^color(red)(4)) =`

`v^4/(2u^3)`