Answer:

Explanation:
So the first step is to add like terms since you can simplify the numerator by adding the two values sine they have the same variable and degree.
Add like terms:
![[(8x^9)/(2x)]^5](https://img.qammunity.org/2023/formulas/mathematics/college/s7ltalkipicmccmjw3fm0cca9gmcodr864.png)
Divide by 2x (divide coefficient by 2, subtract coefficient degrees)
![[4x^8]^5](https://img.qammunity.org/2023/formulas/mathematics/college/bbcqizo9kdp2qahh2532ha82oduj5lbc9p.png)
Multiply exponents and raise 4 to the power of 5

The reason you multiply exponents is because you can think about it like this:
(4 * x * x * x * x * x * x * x * x) (this has one 4 and 8 x's because x is raised to the power of 8. Now if you do that 5 times which is what the exponent is doing you're going to have 40 x's and 8 4's. So it's essentially
(4 * x * x * x * x * x * x * x * x) * (4 * x * x * x * x * x * x * x * x) * (4 * x * x * x * x * x * x * x * x) * (4 * x * x * x * x * x * x * x * x) * (4 * x * x * x * x * x * x * x * x). If you group like terms you'll get (4 * 4 * 4 * 4 * 4) * (x * x * x * x * x * x * x * x * x * x * x * x * x * x * x * x * x * x * x * x * x * x * x * x * x * x * x * x * x * x * x * x * x * x * x * x * x * x * x * x * x * x * x * x * x). Which simplifies to 4^5 * x ^ (8 * 5) which further simplifies to the answer 1024x^40