Question

How do you simplify `((4a³b)/(a²b³)) * ((3b²)/(2a²b^4))`?

Answer 1

`((4a³b)/(a²b³)) * ((3b²)/(2a²b^4)) = color(green)(6/( a *b^4)`

Explanation:

We know that `color(blue)(a^m/a^n = a^(m-n)`

First, we combine the constants and the common variables together
`((4a³b)/(a²b³)) * ((3b²)/(2a²b^4))`
`= ((4*3)/2) * (a^3/(a^2*a^2)) * ((b*b^2)/(b^3*b^4))`

We know that `color(blue)((x^m*x^n) = x^(m+n)`

`= 6 * (a^3/(a^(2+2))) * (b^(1+2)/(b^(3+4)))`

`= 6 * (a^3/(a^4)) * (b^3/(b^7))`

We also know that `color(blue)(x^m/x^n = x^(m-n)`

`= 6 * (a^(3-4)) * (b^(3-7))`

`= 6* a^-1 *b^-4`

We know that `color(blue)(x^-m = 1/x^m`

`= 6/( a *b^4)`