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:

$e^{14}s^{13}$