Simplify 12 {a}^(4) {b}^( - 3) / 15 {a}^( - 2) b I don't understand what the lesson is trying to teach me.

Question

simplify
`12 {a}^(4) {b}^( - 3) / 15 {a}^( - 2) b` I don't understand what the lesson is trying to teach me.

Answer 1

To do the divisions, we divide all the same terms together.

12 : 15 = 4/5
a^4 : a^-2 = a^4 - (-2) = a^6
b^-3 : b = b^-3 - (1) = b^-4

And do the last step of moving the terms with negative exponents, we get the result shown in the picture.

Answer 2

We have to simplify the expression:

`(12a^4b^(-3))/(15a^(-2)b)`

We have the variables a and b with different exponents, that we can simplify applyinf the rules of the exponents.

For example, we can do this:

`\begin{gathered} (12a^4b^(-3))/(15a^(-2)b) \\ (12)/(15)a^(4-(-2))b^(-3-1) \\ (4)/(5)a^6b^(-4) \\ (4)/(5)(a^6)/(b^4) \end{gathered}`

Answer: (4/5)*a^6/b^4