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