# One third power

Which equation justifies why ten to the one-third power equals the cube root of ten?

Result

x =  0

#### Solution:

$10^{ 1 / 3 } = \sqrt[\\3]{ 10 } \ \\ 10^{ n/m } = \sqrt[m](10^n) \ \\ n = 1 \ \\ m = 3 \ \\ \ \\ \ \\ (10^{ x })^{ y } = 10^{ x \cdot \ y } \ \\ \ \\ \text{ Correctness test: } \ \\ \ \\ (10^{ 1 / 3 })^{ 3 } = 10^{ 3 \cdot \ \dfrac{ 1 }{ 3 } } = 10^{ 1 } = 10 \ \\ \ \\ x = 0$

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