Exponents: Rational exponents

Exponents: Rational exponents

Lessons

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}
  • 1.
    prove: a38=8a3a^{3 \over 8} = {^8}\sqrt{a^3}

  • 2.
    Simplifying Expressions Using: nx=x1n{^n}\sqrt{x}=x^{\frac{1}{n}}
    Simplify the following expressions if possible.
    a)
    641364^{\frac{1}{3}}
    161416^{\frac{1}{4}}

    b)
    (16)14(-16)^{\frac{1}{4}}
    (32)15(-32)^{\frac{1}{5}}


  • 3.
    evaluate:
    a)
    (25)12(25)^{1 \over 2}

    b)
    (4)12(-4)^{1 \over 2}

    c)
    (10)38(10)^{3 \over 8}

    d)
    (8)53(8)^{5 \over 3}

    e)
    (24332)25(-{243 \over 32})^{-{2 \over 5}}


  • 4.
    Simplifying Expressions Using: x1n=1x1n=1nxx^{-\frac{1}{n}}=\frac{1}{x^{\frac{1}{n}}}=\frac{1}{{^n}\sqrt{x}}
    Simplify the following expressions.
    a)
    2713 27^{-\frac{1}{3}}

    b)
    16x\frac{1}{{^6}\sqrt{x}}

    c)
    (64x8)12(64x^8)^{-\frac{1}{2}}


  • 5.
    Simplifying Expressions Using: xmn=nxmx^{\frac{m}{n}}={^n}\sqrt{x^m}
    Simplify the following expressions if possible.
    a)
    2x6{^2}\sqrt{x^6}

    b)
    2532 25^{\frac{3}{2}}

    c)
    (125)23 (-125)^{-\frac{2}{3}}

    d)
    36x16y24 \sqrt{36x^{16}y^{24}}

    e)
    3216a9b24c117{^3}\sqrt{-216a^9b^{24}c^{117}}