Question

How do you simplify `\frac { 100a ^ { 2} b ^ { 4} } { 5a b ^ { 2} }`?

Answer 1

See the entire solution process below:

Explanation:

First, rewrite the expression as:

`(100/5)(a^2/a)(b^4/b^2) -> 20(a^2/a)(b^4/b^2)`

Now, use these two rules of exponents to simplify the `a` and `b` terms:

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

`20(a^2/a)(b^4/b^2) -> 20(a^color(red)(2)/a^color(blue)(1))(b^color(red)(4)/b^color(blue)(2)) -> 20a^(color(red)(2)-color(blue)(1))b^(color(red)(4)-color(blue)(2)) ->`

`20a^1b^2`

We can use the opposite of this rule: `a = a^color(blue)(1)` or `a^color(blue)(1) = a`, to complete the simplification:

`20a^color(blue)(1)b^2 =`20ab^2##