Question

Question #1a422

Answer 1

`(12a^(-2)bc^(-2))/(3a^3b^(-3))=color(red)((4b^4)/(a^5c^2))`

Explanation:

Remember that `color(blue)(b^(-a)=1/(b^a))` and `color(blue)(1/b^(-a)=b^a)`

`(12a^(-2)bc^(-2))/(3a^3b^(-3)` can be decomposed as:
`color(white)("XXX")12 * a^(-2) * b * c^(-2) * 1/3 * 1/(a^3) * 1/(b^(-3))`

Using our remembrance
`color(white)("XXX")=12 * 1/(a^2) * b * 1/(c^2) * 1/3 * 1/(a^3) * b^3`

Grouping like factors:
`color(white)("XXX")=underbrace(12 * 1/3) * underbrace(1/(a^2) * 1/(a^3)) * underbrace(b * b^3) * underbrace(1/(c^2))`

Combining like factors:
`color(white)("XXX")=4 * 1/(a^5) * b^4 * 1/(c^2)`

Writing in "compressed form"
`color(white)("XXX")=(4b^4)/(a^5c^2)`