Question

How do you simplify `\frac { k ^ { 8} ( k ^ { 4} ) ^ { 5} } { 10m ^ { 8} ( 2m ^ { 2} ) ^ { 3} }`?

Answer 1

`(k^28)/(60+10m^6+6m^8+m^14)`

Explanation:

We start at the top.
`k^8 (k^4)^5`
To get rid of the brackets, we start with `(k^4)^5`
it's `k^4` 5 times, so in short, it's `k^20`
What we have left is `k^8*k^20` which equals `k^28`

Now the bottom.
Same thing here, brackets first: `(2m^2)^3`
`2m^2` three times, in short, `6m^6`
We now need to break up `10m^8(6m^6)`
`10m^8(6m^6)= 60+10m^6+6m^8+m^14`

Now we add this to the answer
(see answer above)