Question

How do you simplify the expression `(x^5y^-8)/(x^5y^-6)` using the properties?

Answer 1

See a solution process below:

Explanation:

First, we can use these two properties of exponents:

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

`(x^color(red)(5)y^color(red)(-8))/(x^color(blue)(5)y^color(blue)(-6)) => x^(color(red)(5)-color(blue)(5))/y^(color(blue)(-6)-color(red)(-8)) => x^(color(red)(5)-color(blue)(5))/y^(color(blue)(-6)+color(red)(8)) => x^0/y^2`

We can use this property to simplify the `x` term:

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

`x^color(red)(0)/y^2 => 1/y^2`