Question

Simplify (e^5 s^3)^2 e^4 s^7 Write your answer with only positive exponents.

Answer 1

To simplify, we will need to use the properties:

`\begin{gathered} (a^bc^d)^f=a^(bf)c^(df) \\ a^b\cdot a^c=a^(b+c) \end{gathered}`

Applying the first property, we have:

`(e^5s^3)^2e^4s^7=e^(5\cdot2)s^(3\cdot2)e^4s^7=e^(10)s^6e^4s^7`

Now, we can rearrenge the multiplications and apply the second property:

`e^(10)s^6e^4s^7=e^(10)e^4s^6s^7=e^(10+4)s^(6+7)=e^(14)s^(13)`

So, the simplification is:

`e^(14)s^(13)`