Question

How do you simplify `(12m^-4p^2)/(-15m^3p^-9)`?

Answer 1

See a solution process below:

Explanation:

First, rewrite the expression as:

`(12/-15)(m^-4/m^3)(p^2/p^-9) => -(3 xx 4)/(3 xx 5)(m^-4/m^3)(p^2/p^-9) =>`

`-(color(red)(cancel(color(black)(3))) xx 4)/(color(red)(cancel(color(black)(3))) xx 5)(m^-4/m^3)(p^2/p^-9) =>`

`-4/5(m^-4/m^3)(p^2/p^-9)`

Next, use this rule for exponents to simplify the `m` terms:

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

`-4/5(m^color(red)(-4)/m^color(blue)(3))(p^2/p^-9) => -4/5(1/m^(color(blue)(3)-color(red)(-4)))(p^2/p^-9) =>`

`-4/5(1/m^(color(blue)(3)+color(red)(4)))(p^2/p^-9) => -4/5(1/m^7)(p^2/p^-9) =>`

`-4/(5m^7)(p^2/p^-9)`

Now, use this rule for exponents to simplify the `p` terms:

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

`-4/(5m^7)(p^color(red)(2)/p^color(blue)(-9)) => -4/(5m^7)p^(color(red)(2)-color(blue)(-9)) => -4/(5m^7)p^(color(red)(2)+color(blue)(9)) =>`

`-4/(5m^7)p^11 =>`

`-(4p^11)/(5m^7)`

Answer 2

Factor and divide out common terms

Explanation:

`12 m^-4p^2 = 3 xx 4 xx 1/m^4 xx p^2`

`15 m^3 p^-9 = 3xx 5 xx m^3 xx 1/p^9`

Putting this a complex fraction gives

`{ (3 xx 4 xx p^2)/(m^4)}/{(3 xx 5 xx m^3)/(p^9)`

Multiplying both the top and the bottom by the inverse of the bottom gives

`{ (3 xx 4 xx p^2) xx (p^9)} / {(m^4) xx( 3 xx 5 xx m^3)}`

dividing out common terms and combining common terms gives

`( 4 xx p^11)/( 5 xx m^7)`

Answer 3

`(4p^11)/(-5m^7)`

Explanation:

`(12m^-4p^2)/(-15m^3p^-9)`

`:.=(cancel12^4p^(2+9))/(cancel(-15)^-5m^(3+4))`

`:.=(4p^11)/(-5m^7)`