Question

How do you simplify `\frac { x y ^ { 0} \cdot ( 3x ^ { 3} y ^ { 3} ) ^ { 0} } { x ^ { 3} y ^ { 3} }`?

Answer 1

See the entire solution process below:

Explanation:

First, use this rule for exponents to simplify the numerator:

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

`(xy^color(red)(0) * (3x^3y^3)^color(red)(0))/(x^3y^3) = (x1 * 1)/(x^3y^3) = x/(x^3y^3)`

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

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

`x/(x^3y^3) = x^color(red)(1)/(x^color(blue)(3)y^3) = 1/(x^(color(blue)(3)-color(red)(1))y^3) = 1/(x^2y^3)`