Power (Algebra)/Rational Number/Examples/8 to the Power of Two Thirds
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Example of Rational Power
- $8^{2/3} = 4$
Proof
| \(\ds 8^{2/3}\) | \(=\) | \(\ds \paren {\paren {2^3}^2}^{1/3}\) | ||||||||||||
| \(\ds \) | \(=\) | \(\ds \paren {4^3}^{1/3}\) | ||||||||||||
| \(\ds \) | \(=\) | \(\ds 4\) |
$\blacksquare$
Sources
- 1977: K.G. Binmore: Mathematical Analysis: A Straightforward Approach ... (previous) ... (next): $\S 1$: Real Numbers: Exercise $\S 1.12 \ (2) \, \text{(i)}$