Question

How do you simplify `a^5/(b^3c^3) div a^4/(b^3c^4)`?

Answer 1

You cancel terms common to the numerator and denominator.

Explanation:

Your expression can be written as

`(a^5)/(b^3c^3) * (b^3c^4)/a^4`

Use the product of powers property of exponents to rewrite the numerators of the two fractions as

`a^5 = a^4 * a`

`b^3 c^4 = b^3c^3 * c`

Your expression will become

`(a^4 * a)/(b^3c^3) * (b^3c^3 * c)/a^4`

Cancel the terms common to the numerator and denominator to get

`(color(red)(cancel(color(black)(a^4))) * a)/(color(blue)(cancel(color(black)(b^3c^3)))) * (color(blue)(cancel(color(black)(b^3c^3))) * c)/(color(red)(cancel(color(black)(a^4)))) = color(green)(ac)`