Question

How do you multiply `\frac { 6a ^ { 5} c } { 5a c ^ { 4} } \times \frac { 4a ^ { 3} } { 9a c ^ { 4} }`?

Answer 1

Multiply all the top numbers and the same for the bottom numbers, just like a regular fraction multiplication. Group like unknowns and add their exponents. You will end up with a single fraction.

Explanation:

We have: `(6a^5c)/(5ac^4)xx(4a^3)/(9ac^4)`

Numbers:
`6xx4=24`
`5xx9=45`

Top:
`a^5xxa^3=a^8`
`cxx1=c`

Bottom:
`axxa=a^2`
`c^4xxc^4=c^8`

Re-assembling:
`(24a^8c)/(45a^2c^8`

Cancelling the divided unknowns exponents by subtraction:
`(24cancel(a^8)a^6cancelc)/(45cancel(a^2)cancel(c^8)c^7`

Then:
`(6a^5c)/(5ac^4)xx(4a^3)/(9ac^4)=(24a^6)/(45c^7)=(8a^6)/(15c^7)`