Power (Algebra)/Rational Number/Examples/0.125 to the Power of Minus Two Thirds

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Example of Rational Power

$0 \cdotp 125^{-2/3} = 4$


Proof

\(\ds 0 \cdotp 125^{-2/3}\) \(=\) \(\ds \paren {\dfrac 1 8}^{-2/3}\)
\(\ds \) \(=\) \(\ds 8^{2/3}\) Definition of Rational Power
\(\ds \) \(=\) \(\ds 64^{1/3}\)
\(\ds \) \(=\) \(\ds \sqrt [3] {64}\)
\(\ds \) \(=\) \(\ds 4\)

$\blacksquare$


Sources