Question

How do you simplify `\frac { 56x ^ { 7} } { 24x ^ { 4} }`?

Answer 1

See a solution process below:

Explanation:

First, rewrite the expression as:

`((8 xx 7)x^7)/((8 xx 3)x^4) => ((color(red)(cancel(color(black)(8))) xx 7)x^7)/((color(red)(cancel(color(black)(8))) xx 3)x^4) => (7x^7)/(3x^4)`

Now, use this rule for exponents to simplify the `x` terms:

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

`(7x^color(red)(7))/(3x^color(blue)(4)) = (7x^(color(red)(7)-color(blue)(4)))/3 = (7x^3)/3` or `7/3x^3`