Exponents: Rational exponents

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Examples
Lessons
  1. prove: a38=8a3a^{3 \over 8} = {^8}\sqrt{a^3}
    1. Simplifying Expressions Using: nx=x1n{^n}\sqrt{x}=x^{\frac{1}{n}}
      Simplify the following expressions if possible.
      1. 641364^{\frac{1}{3}}
        161416^{\frac{1}{4}}
      2. (−16)14(-16)^{\frac{1}{4}}
        (−32)15(-32)^{\frac{1}{5}}
    2. evaluate:
      1. (25)12(25)^{1 \over 2}
      2. (−4)12(-4)^{1 \over 2}
      3. (10)38(10)^{3 \over 8}
      4. (8)53(8)^{5 \over 3}
      5. (−24332)−25(-{243 \over 32})^{-{2 \over 5}}
    3. Simplifying Expressions Using: x−1n=1x1n=1nxx^{-\frac{1}{n}}=\frac{1}{x^{\frac{1}{n}}}=\frac{1}{{^n}\sqrt{x}}
      Simplify the following expressions.
      1. 27−13 27^{-\frac{1}{3}}
      2. 16x\frac{1}{{^6}\sqrt{x}}
      3. (64x8)−12(64x^8)^{-\frac{1}{2}}
    4. Simplifying Expressions Using: xmn=nxmx^{\frac{m}{n}}={^n}\sqrt{x^m}
      Simplify the following expressions if possible.
      1. 2x6{^2}\sqrt{x^6}
      2. 2532 25^{\frac{3}{2}}
      3. (−125)−23 (-125)^{-\frac{2}{3}}
      4. 36x16y24 \sqrt{36x^{16}y^{24}}
      5. 3−216a9b24c117{^3}\sqrt{-216a^9b^{24}c^{117}}
    Topic Notes
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    • nx=x1n{^n}\sqrt{x}=x^{\frac{1}{n}}
    • x−1n=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}
    Basic Concepts
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    Related Concepts
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