Question

How do you simplify `(4m^4n^3p^3)/(3m^2n^2p^4)` and write it using only positive exponents?

Answer 1

See the entire simplification process below:

Explanation:

First, rewrite as:

`(4/3)(m^4/m^2)(n^3/n^2)(p^3/p^4)`

Now, use these rules of exponents to begin the simplification:

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

`(4/3)(m^color(red)(4)/m^color(blue)(2))(n^color(red)(3)/n^color(blue)(2))(p^color(red)(3)/p^color(blue)(4)) = (4/3)(m^(color(red)(4)-color(blue)(2)))(n^(color(red)(3)-color(blue)(2)))(1/p^(color(blue)(4)-color(red)(3))) =`

`(4m^2n^1)/(3p^1)`

We can use this rule of exponents to complete the simplification:

`a^color(red)(1) = a`

`(4m^2n^color(red)(1))/(3p^color(red)(1)) = (4m^2n)/(3p)`