Question

Simplify c^4(xc^4) ^4 s^4 x Write your answer with only positive exponents

Answer 1

Firstly, let's put the varibles without exponent the exponent 1:

`c^4(xc^4)^4s^4x=c^4(x^1c^4)^4s^4x^1`

Now, we can apply the Power to a Power rule:

`(a^bc^d)^f=a^(b\cdot f)c^(d\cdot f)`
`c^4(x^1c^4)^4s^4x^1=c^4x^(1\cdot4)c^(4\cdot4)s^4x^1=c^4x^4c^(16)s^4x^1`

Now, we can rearregent them to get the variables paired:

`c^4x^4c^(16)s^4x^1=c^4c^(16)x^4x^1s^4`

And now we use the Power of a Product rule:

`a^ba^c=a^(b+c)`

So:

`c^4c^(16)x^4x^1s^4=c^(4+16)x^(4+1)s^4=c^(20)x^5s^4`

So, the simplification is:

`c^(20)x^5s^4`