Exponents: Rational exponents

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Now Playing:Rational exponents– Example 1
Examples
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  1. prove: a38=8a3a^{3 \over 8} = {^8}\sqrt{a^3}
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    Exponents: Product rule (a^x)(a^y) = a^(x+y)
    Notes
    nx=x1n{^n}\sqrt{x}=x^{\frac{1}{n}}
    x1n=1x1n=1nxx^{-\frac{1}{n}}=\frac{1}{x^{\frac{1}{n}}}=\frac{1}{{^n}\sqrt{x}}
    xmn=nxmx^{\frac{m}{n}}={^n}\sqrt{x^m}