Question

How do you simplify `\frac { 3x ^ { - 2} y ^ { 3} } { 9x ^ { 4} y ^ { 5} }`?

Answer 1

See a solution process below:

Explanation:

First, rewrite this expression as:

`3/9(x^-2/x^4)(y^3/y^5) => 1/3(x^-2/x^4)(y^3/y^5)`

Next, use this rule of exponents to simplify the `x` term:

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

`1/3(x^color(red)(-2)/x^color(blue)(4))(y^3/y^5) => 1/3(1/x^(color(blue)(4)-color(red)(-2)))(y^3/y^5) =>`

`1/3(1/x^(color(blue)(4)+color(red)(2)))(y^3/y^5) => 1/3(1/x^(color(blue)(6)))(y^3/y^5) => 1/(3x^6)(y^3/y^5)`

Now, use this same rule to simplify the `y` term:

`1/(3x^6)(y^color(red)(3)/y^color(blue)(5)) => 1/(3x^6)(1/y^(color(blue)(5)-color(red)(3))) => 1/(3x^6)(1/y^2) =>`

`1/(3x^6y^2)`