Question

How do you divide `\frac { 6x ^ { - 5} y ^ { - 5} } { 12x ^ { 4} y }`?

Answer 1

See a solution process below:

Explanation:

First, rewrite the expression as:

`(6/12)(x^-5/x^4)(y^-5/y) => 1/2(x^-5/x^4)(y^-5/y)`

Next, use this rule of exponents to divide the `x` terms:

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

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

`1/2(1/(x^(color(blue)(4)+color(red)(5))))(y^-5/y) => 1/2(1/(x^9))(y^-5/y) =>`

`1/(2x^9)(y^-5/y)`

Now, use these rules of exponents to divide the `y` terms:

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

`1/(2x^9)(y^-5/y) => 1/(2x^9)(y^color(red)(-5)/y^color(blue)(1)) => 1/(2x^9)(1/y^(color(blue)(1)-color(red)(-5))) =>`

`1/(2x^9)(1/y^(color(blue)(1)+color(red)(5))) => 1/(2x^9)(1/y^6) =>`

`1/(2x^9y^6)`