Which equation justifies why ten to the one third power equals the cube root of ten?
2 answers:
For this case we must find the justification of:
![10 ^ {\frac {1} {3}} = \sqrt [3] {10}](https://tex.z-dn.net/?f=10%20%5E%20%7B%5Cfrac%20%7B1%7D%20%7B3%7D%7D%20%3D%20%5Csqrt%20%5B3%5D%20%7B10%7D)
By definition of properties of powers and roots we have to meet:
![a ^ {\frac {m} {n}} = \sqrt [n] {a ^ m}](https://tex.z-dn.net/?f=a%20%5E%20%7B%5Cfrac%20%7Bm%7D%20%7Bn%7D%7D%20%3D%20%5Csqrt%20%5Bn%5D%20%7Ba%20%5E%20m%7D)
So, if we have:
![\sqrt [3] {10} = \ \sqrt [3] {10 ^ 1} = 10 ^ {\frac {1} {3}}](https://tex.z-dn.net/?f=%5Csqrt%20%5B3%5D%20%7B10%7D%20%3D%20%5C%20%5Csqrt%20%5B3%5D%20%7B10%20%5E%201%7D%20%3D%2010%20%5E%20%7B%5Cfrac%20%7B1%7D%20%7B3%7D%7D)
Other property states that:
![(a ^ n) ^ m = a ^ {n * m}](https://tex.z-dn.net/?f=%28a%20%5E%20n%29%20%5E%20m%20%3D%20a%20%5E%20%7Bn%20%2A%20m%7D)
So, the expression: "Ten to the one third power all raised to the third power" is represented as:
![(10 ^{\frac {1} {3}}) ^ 3 = 10 ^ {\frac {3*1} {3}} = 10 ^ 1 = 10](https://tex.z-dn.net/?f=%2810%20%5E%7B%5Cfrac%20%7B1%7D%20%7B3%7D%7D%29%20%5E%203%20%3D%2010%20%5E%20%7B%5Cfrac%20%7B3%2A1%7D%20%7B3%7D%7D%20%3D%2010%20%5E%201%20%3D%2010)
ANswer;
Option B
Answer: The answer would be (10^1/3)³ = 10 ^(1/3×3) =10
Step-by-step explanation:
I took the test on FLVS
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