Answer:
The lower bound of 19.4 is 19.35
Answer:
wat is this, my g this looks like a test
Answer: 83/100 or .83
Step-by-step explanation:
Answer:
Option (b) is correct.
![(2^\frac{1}{4} )^4=2^\frac{1}{4} \times 2^\frac{1}{4}\times 2^\frac{1}{4}\times 2^\frac{1}{4}=2^{(\frac{1}{4}+ \frac{1}{4}+ \frac{1}{4}+ \frac{1}{4} )}=2^{1}=2](https://tex.z-dn.net/?f=%282%5E%5Cfrac%7B1%7D%7B4%7D%20%29%5E4%3D2%5E%5Cfrac%7B1%7D%7B4%7D%20%5Ctimes%202%5E%5Cfrac%7B1%7D%7B4%7D%5Ctimes%202%5E%5Cfrac%7B1%7D%7B4%7D%5Ctimes%202%5E%5Cfrac%7B1%7D%7B4%7D%3D2%5E%7B%28%5Cfrac%7B1%7D%7B4%7D%2B%20%5Cfrac%7B1%7D%7B4%7D%2B%20%5Cfrac%7B1%7D%7B4%7D%2B%20%5Cfrac%7B1%7D%7B4%7D%20%29%7D%3D2%5E%7B1%7D%3D2)
Step-by-step explanation:
Given: ![(2^\frac{1}{4} )^4](https://tex.z-dn.net/?f=%282%5E%5Cfrac%7B1%7D%7B4%7D%20%29%5E4)
We have too choose the correct simplification for the given statement.
Consider ![(2^\frac{1}{4} )^4](https://tex.z-dn.net/?f=%282%5E%5Cfrac%7B1%7D%7B4%7D%20%29%5E4)
Using property of exponents,
We have,
![(2^\frac{1}{4} )^4=2^\frac{1}{4} \times 2^\frac{1}{4}\times 2^\frac{1}{4}\times 2^\frac{1}{4}](https://tex.z-dn.net/?f=%282%5E%5Cfrac%7B1%7D%7B4%7D%20%29%5E4%3D2%5E%5Cfrac%7B1%7D%7B4%7D%20%5Ctimes%202%5E%5Cfrac%7B1%7D%7B4%7D%5Ctimes%202%5E%5Cfrac%7B1%7D%7B4%7D%5Ctimes%202%5E%5Cfrac%7B1%7D%7B4%7D)
Again applying property of exponents ![a^m\times a^m=a^{n+m}](https://tex.z-dn.net/?f=a%5Em%5Ctimes%20a%5Em%3Da%5E%7Bn%2Bm%7D)
We have,
![(2^\frac{1}{4} )^4=2^{(\frac{1}{4}+ \frac{1}{4}+ \frac{1}{4}+ \frac{1}{4} )}](https://tex.z-dn.net/?f=%282%5E%5Cfrac%7B1%7D%7B4%7D%20%29%5E4%3D2%5E%7B%28%5Cfrac%7B1%7D%7B4%7D%2B%20%5Cfrac%7B1%7D%7B4%7D%2B%20%5Cfrac%7B1%7D%7B4%7D%2B%20%5Cfrac%7B1%7D%7B4%7D%20%29%7D)
Simplify, we have,
![(2^\frac{1}{4} )^4=2^{\frac{4}{4}}](https://tex.z-dn.net/?f=%282%5E%5Cfrac%7B1%7D%7B4%7D%20%29%5E4%3D2%5E%7B%5Cfrac%7B4%7D%7B4%7D%7D)
we get,
![(2^\frac{1}{4} )^4=2^{1}=2](https://tex.z-dn.net/?f=%282%5E%5Cfrac%7B1%7D%7B4%7D%20%29%5E4%3D2%5E%7B1%7D%3D2)
Thus, ![(2^\frac{1}{4} )^4=2](https://tex.z-dn.net/?f=%282%5E%5Cfrac%7B1%7D%7B4%7D%20%29%5E4%3D2)
Option (b) is correct.