Answer:
![\sqrt{3} + \frac{5\sqrt{3} }{6}](https://tex.z-dn.net/?f=%5Csqrt%7B3%7D%20%2B%20%5Cfrac%7B5%5Csqrt%7B3%7D%20%7D%7B6%7D)
Step-by-step explanation:
tan(30°) = ![\frac{\sqrt{3}}{3}](https://tex.z-dn.net/?f=%5Cfrac%7B%5Csqrt%7B3%7D%7D%7B3%7D)
cot(30°) = ![\sqrt{3}](https://tex.z-dn.net/?f=%5Csqrt%7B3%7D)
sin(60°) = ![\frac{\sqrt{3}}{2}](https://tex.z-dn.net/?f=%5Cfrac%7B%5Csqrt%7B3%7D%7D%7B2%7D)
![\frac{\sqrt{3} }{3} +\sqrt{3} +\frac{\sqrt{3}}{2} = \sqrt{3} +\frac{5\sqrt{3} }{6}](https://tex.z-dn.net/?f=%5Cfrac%7B%5Csqrt%7B3%7D%20%7D%7B3%7D%20%2B%5Csqrt%7B3%7D%20%2B%5Cfrac%7B%5Csqrt%7B3%7D%7D%7B2%7D%20%20%3D%20%5Csqrt%7B3%7D%20%2B%5Cfrac%7B5%5Csqrt%7B3%7D%20%7D%7B6%7D)
Answer:
1. A. 1
2. D. ![17^9](https://tex.z-dn.net/?f=17%5E9)
Step-by-step explanation:
Properties used:
- Power of a Power Property
- Product Property
- Quotient Property
- Zero Exponent Property
1. First, let's deal with the numerator.
can be turned into
by using the Power of a Power Property.
And then use the Product Property, ![(17^1^8)(17^-^1^0) = 17^8](https://tex.z-dn.net/?f=%2817%5E1%5E8%29%2817%5E-%5E1%5E0%29%20%3D%2017%5E8)
So now, our fraction is this: ![\frac{17^8}{17^8}](https://tex.z-dn.net/?f=%5Cfrac%7B17%5E8%7D%7B17%5E8%7D)
All number over itself in a fraction is equal to 1. But you can also do this the mathmatic way using the Quotient Property:
or
. Which then you plug the numbers in:
. And since we know that in Zero Exponent Property:
, we can see that
. So either way, we get 1.
So the answer is 1, which is A
2. Power of a Power Property: ![(a^m)^n = a^m^n](https://tex.z-dn.net/?f=%28a%5Em%29%5En%20%3D%20a%5Em%5En)
So plug the numbers in the property:
= ![17^1^8](https://tex.z-dn.net/?f=17%5E1%5E8)
Product Property: ![(a^m)(a^n) = a^m^+^n](https://tex.z-dn.net/?f=%28a%5Em%29%28a%5En%29%20%3D%20a%5Em%5E%2B%5En)
We plug the equation in with
turned into
---
![(17^1^8)(17^-^9) = 17^1^8^-^9 = 17^9](https://tex.z-dn.net/?f=%2817%5E1%5E8%29%2817%5E-%5E9%29%20%3D%2017%5E1%5E8%5E-%5E9%20%3D%2017%5E9)
So the answer is
, which is D
I hope this helps!
Please give Brainliest!
Have a great day!
OH I KNOW I KNOW TEACHER. its its wait im in middle school what the heck am i doing in here.