Power (Algebra)/Rational Number/Examples/32 to the Power of Six Fifths
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Example of Rational Power
- $32^{6/5} = 64$
Proof
| \(\ds 32^{6/5}\) | \(=\) | \(\ds \paren {\paren {2^5}^6}^{1/5}\) | ||||||||||||
| \(\ds \) | \(=\) | \(\ds 2^6\) | ||||||||||||
| \(\ds \) | \(=\) | \(\ds 64\) |
$\blacksquare$
Sources
- 1977: K.G. Binmore: Mathematical Analysis: A Straightforward Approach ... (previous) ... (next): $\S 1$: Real Numbers: Exercise $\S 1.12 \ (2) \, \text{(iii)}$