Question

How do you simplify `(343 u^4 c^-5) /(7 u^6 c^-3)^-5`?

Answer 1

`(5764801u^34)/(c^20)`

Explanation:

There is a negative exponent rule, I'm not quite sure if it has a name, but it says that a negative exponent in the numerator can be moved to the denominator and become positive, and vice versa.
An example would be `x^-2=1/x^2`

So using this

`((7u^6c^-3)^5(343u^4))/c^5`

Then we can distribute the exponent, `5`, in the numerator
`(16807u^30c^-15(343u^4))/c^5`

Now we can move the `c^-15` to the denominator using the negative exponent rule
`(16807u^30(343u^4))/(c^5*c^15)`

We can now combine like bases

`(5764801u^34)/(c^20)`

Answer 2

`(x^a)^b=x^(axxb)`

`[343u^4c^-5]/(7u^6c^-3)^-5=[7^3u^4c^-5]/(7^-5u^-30c^15)`

`x^a/x^b=x^(a-b)`

`7^8u^34c^-20`

or `[7^8u^34]/c^20`

Answer 3

`(7^8u^34)/(c^20)`

Explanation:

`(343u^4c^-5)/(7u^6c^-3)^-5`

Use the law of indices for negative indices:

`x^-m = 1/x^m`

`=(343u^4xx(7u^6c^-3)^5)/c^5`

Note that `343 = 7^3`

It is better to keep the numbers in index form.

`=(7^3u^4 xx 7^5u^30c^-15)/c^5`

`=(7^3u^4 xx 7^5u^30)/(c^5 xxc^15)`

Add the indices of like bases:

`=(7^8u^34)/(c^20)`