Power (Algebra)/Rational Number/Examples/27 to the Power of Minus Four Thirds
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Example of Rational Power
- $27^{-4/3} = \dfrac 1 {81}$
Proof
\(\ds 27^{-4/3}\) | \(=\) | \(\ds \paren {\dfrac 1 {27^4} }^{1/3}\) | ||||||||||||
\(\ds \) | \(=\) | \(\ds \paren {\dfrac 1 {\paren {3^3}^4} }^{1/3}\) | ||||||||||||
\(\ds \) | \(=\) | \(\ds \paren {\paren {\dfrac 1 {3^4} }^3}^{1/3}\) | ||||||||||||
\(\ds \) | \(=\) | \(\ds \dfrac 1 {81}\) |
$\blacksquare$
Sources
- 1977: K.G. Binmore: Mathematical Analysis: A Straightforward Approach ... (previous) ... (next): $\S 1$: Real Numbers: Exercise $\S 1.12 \ (2) \, \text{(ii)}$