Question

How do you divide `\frac { 5x ^ { 9} } { 2x ^ { 3} } \div \frac { 20x } { 8x ^ { 5} }`?

Answer 1

`color(green)(x^10)`

Explanation:

Remember that dividing can be done as multiplication by the inverse,
so `(5x^9)/(2x^3)div(20x)/(8x^5) = (5x^9)/(2x^3)xx(8x^5)/(20x)`

with some cancelling:
`color(white)("XXX")=(5x^(cancel(9)^6))/(2cancel(x^3))xx(8x^(cancel(5)^4))/(20cancel(x))`

`color(white)("XXX")=(cancel(5)x^6)/2xx(8x^4)/(cancel(20)_4)`

`color(white)("XXX")=(x^6)/cancel(2)xx(cancel(8)^4x^4)/4`

`color(white)("XXX")=x^6/1 xx (cancel(4)x^4)/cancel(4)`

`color(white)("XXX")=x^6xxx^4`

`color(white)("XXX")=x^10`