Question

How do you divide `\frac { 15a ^ { 5} b ^ { 2} } { 5a ^ { 2} b }`?

Answer 1

See a solution process below:

Explanation:

First, rewrite the expression as:

`(15/5)(a^5/a^2)(b^2/b) => 3(a^5/a^2)(b^2/b)`

Now, use this rule of exponents to divide the `a` term:

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

`3(a^color(red)(5)/a^color(blue)(2))(b^2/b) => 3a^(color(red)(5)-color(blue)(2))(b^2/b) => 3a^3(b^2/b)`

Now, use these rules of exponents to divide the `b` terms:

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

`3a^3(b^2/b) => 3a^3(b^color(red)(2)/b^color(blue)(1)) => 3a^3b^(color(red)(2)-color(blue)(1)) => 3a^3b^1 =>`

`3a^3b`