Question

How do you simplify `(-3m^4n)/(12m^6n^4)`?

Answer 1

See a solution process below:

Explanation:

First, rewrite the expression as:

`(-3/12)(m^4/m^6)(n/n^4) => -1/4(m^4/m^6)(n/n^4)`

Next, use this rule of exponents to rewrite the numerator for the `n` term:

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

`-1/4(m^4/m^6)(n^color(red)(1)/n^4)`

Now, use this rule of exponents to complete the simplification for the `m` and `n` terms:

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

`-1/4(m^color(red)(4)/m^color(blue)(6))(n^color(red)(1)/n^color(blue)(4)) =>`

`-1/4(1/m^(color(blue)(6)-color(red)(4)))(1/n^(color(blue)(4)-color(red)(1))) =>`

`-1/4(1/m^2)(1/n^3) =>`

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