Question

How do you simplify `[\frac { 12x ^ { 8} y ^ { 3} } { 9x ^ { - 3} y ^ { 5} } ]`?

Answer 1

See a solution process below:

Explanation:

First, rewrite the expression as:

`12/9(x^8/x^-3)(y^3/y^5) =>`

`(3 xx 4)/(3 xx 3)(x^8/x^-3)(y^3/y^5) =>`

`(color(red)(cancel(color(black)(3))) xx 4)/(color(red)(cancel(color(black)(3))) xx 3)(x^8/x^-3)(y^3/y^5) =>`

`4/3(x^8/x^-3)(y^3/y^5)`

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

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

`4/3(x^color(red)(8)/x^color(blue)(-3))(y^3/y^5) =>`

`4/3x^(color(red)(8)-color(blue)(-3))(y^3/y^5) =>`

`4/3x^(color(red)(8)+color(blue)(3))(y^3/y^5) =>`

`4/3x^11(y^3/y^5) =>`

`(4x^11)/3(y^3/y^5)`

Now, use this rule of exponents to simplify the `y` terms:

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

`(4x^11)/3(y^color(red)(3)/y^color(blue)(5)) =>`

`(4x^11)/3 1/y^(color(blue)(5)-color(red)(3)) =>`

`(4x^11)/3 1/y^2 =>`

`(4x^11)/(3y^2) =>`