Answer:
See explanation
Step-by-step explanation:
1. To rewrite the expression
![(4^{\frac{2}{5}})^{\frac{1}{4}},](https://tex.z-dn.net/?f=%284%5E%7B%5Cfrac%7B2%7D%7B5%7D%7D%29%5E%7B%5Cfrac%7B1%7D%7B4%7D%7D%2C)
use exponents property
![(a^m)^n=a^{m\cdot n}](https://tex.z-dn.net/?f=%28a%5Em%29%5En%3Da%5E%7Bm%5Ccdot%20n%7D)
So,
![(4^{\frac{2}{5}})^{\frac{1}{4}}=4^{\frac{2}{5}\cdot \frac{1}{4}}=4^{\frac{2}{20}}=4^{\frac{1}{10}}](https://tex.z-dn.net/?f=%284%5E%7B%5Cfrac%7B2%7D%7B5%7D%7D%29%5E%7B%5Cfrac%7B1%7D%7B4%7D%7D%3D4%5E%7B%5Cfrac%7B2%7D%7B5%7D%5Ccdot%20%5Cfrac%7B1%7D%7B4%7D%7D%3D4%5E%7B%5Cfrac%7B2%7D%7B20%7D%7D%3D4%5E%7B%5Cfrac%7B1%7D%7B10%7D%7D)
2. Why ![10^{\frac{1}{3}}=\sqrt[3]{10}?](https://tex.z-dn.net/?f=10%5E%7B%5Cfrac%7B1%7D%7B3%7D%7D%3D%5Csqrt%5B3%5D%7B10%7D%3F)
Raise both sides to 10 power:
![(10^{\frac{1}{3}})^3=10^{\frac{1}{3}\cdot 3}=10^1=10\\ \\(\sqrt[3]{10})^3=10](https://tex.z-dn.net/?f=%2810%5E%7B%5Cfrac%7B1%7D%7B3%7D%7D%29%5E3%3D10%5E%7B%5Cfrac%7B1%7D%7B3%7D%5Ccdot%203%7D%3D10%5E1%3D10%5C%5C%20%5C%5C%28%5Csqrt%5B3%5D%7B10%7D%29%5E3%3D10)
So,
![(10^{\frac{1}{3}})^3=(\sqrt[3]{10} )^3](https://tex.z-dn.net/?f=%2810%5E%7B%5Cfrac%7B1%7D%7B3%7D%7D%29%5E3%3D%28%5Csqrt%5B3%5D%7B10%7D%20%29%5E3)
3. Simplify ![\dfrac{3^4}{9}](https://tex.z-dn.net/?f=%5Cdfrac%7B3%5E4%7D%7B9%7D)
Use the Quotient of Powers Property:
![\dfrac{a^m}{a^n}=a^{m-n}](https://tex.z-dn.net/?f=%5Cdfrac%7Ba%5Em%7D%7Ba%5En%7D%3Da%5E%7Bm-n%7D)
Then
![\dfrac{3^4}{9}=\dfrac{3^4}{3^2}=3^{4-2}=3^2](https://tex.z-dn.net/?f=%5Cdfrac%7B3%5E4%7D%7B9%7D%3D%5Cdfrac%7B3%5E4%7D%7B3%5E2%7D%3D3%5E%7B4-2%7D%3D3%5E2)
4. Solve ![4\sqrt{2}+5\sqrt{4}](https://tex.z-dn.net/?f=4%5Csqrt%7B2%7D%2B5%5Csqrt%7B4%7D)
First, note that
then
![4\sqrt{2}+5\sqrt{4}=4\sqrt{2}+5\cdot 2=4\sqrt{2}+10](https://tex.z-dn.net/?f=4%5Csqrt%7B2%7D%2B5%5Csqrt%7B4%7D%3D4%5Csqrt%7B2%7D%2B5%5Ccdot%202%3D4%5Csqrt%7B2%7D%2B10)
Number
is irrational number, number 10 is rational number. The sum of irrational and rational numbers is irrational number.
5. The same as option 4.
Answer:
the last one is right by look at the chart
Answer:
?
Step-by-step explanation:
Answer:
![13.65^0.](https://tex.z-dn.net/?f=13.65%5E0.)
Step-by-step explanation:
Given,
Height of tee, H = 43 yard
Direct distance of the hole is, D = 177 yards
Now, Angle of depression of tee
![\tan \theta = \dfrac{H}{D}](https://tex.z-dn.net/?f=%5Ctan%20%5Ctheta%20%3D%20%5Cdfrac%7BH%7D%7BD%7D)
![\tan \theta = \dfrac{43}{177}](https://tex.z-dn.net/?f=%5Ctan%20%5Ctheta%20%3D%20%5Cdfrac%7B43%7D%7B177%7D)
![\tan \theta =0.2429](https://tex.z-dn.net/?f=%5Ctan%20%5Ctheta%20%3D0.2429)
![\theta = 13.65^\circ](https://tex.z-dn.net/?f=%5Ctheta%20%3D%2013.65%5E%5Ccirc)
Hence, angle of depression from tee to the green is ![13.65^0.](https://tex.z-dn.net/?f=13.65%5E0.)