Question

How do you simplify `(10x^4 y^9) /( 30x^12 y^-3)`?

Answer 1

See a solution process below:

Explanation:

First, rewrite the expression as:

`10/30(x^4/x^12)(y^9/y^-3) =>`

`(1color(red)(cancel(color(black)(0))))/(3color(red)(cancel(color(black)(0))))(x^4/x^12)(y^9/y^-3) =>`

`1/3(x^4/x^12)(y^9/y^-3)`

Next, use this rule for 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)(4)/x^color(blue)(12))(y^9/y^-3) =>`

`1/3(1/x^(color(blue)(12)-color(red)(4)))(y^9/y^-3) =>`

`1/3(1/x^8)(y^9/y^-3) =>`

`1/(3x^8)(y^9/y^-3)`

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

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

`1/(3x^8)(y^color(red)(9)/y^color(blue)(-3)) =>`

`1/(3x^8)(y^(color(red)(9)-color(blue)(-3))) =>`

`1/(3x^8)(y^(color(red)(9)+color(blue)(3))) =>`

`1/(3x^8)(y^12) =>`

`y^12/(3x^8)`