Convert between radicals and rational exponents

Convert between radicals and rational exponents

We will learn how to convert between radicals and rational exponents in this lesson. Therefore, it is a good idea to brush up on your understanding of all the basic rules of exponents before stating to watch the lesson.

Lessons

Ax/y=yAx {A^{x/y}} = {^y}\sqrt{A^x}

  • 1.
    Write the following in the radical form
    a)
    2723 {27^{- \frac{2}{3}}}

    b)
    (8)35(-8 {)^{- \frac{3}{5}}}


  • 2.
    Write the answer with positive exponents and then as entire radical
    a)
    (94)34( \frac{9}{4}{)^{- \frac{3}{4}}}

    b)
    (16)45 -(-16 {)^{- \frac{4}{5}}}

    c)
    (5x37)(25x37) \frac{(5 {x^\frac{3}{7}} )}{(25 {x^{- \frac{3}{7}})}}


  • 3.
    Write the answer as a power and evaluate
    a)
    5a3{^5}\sqrt{a^3}

    b)
    1/4a7 1/ {^4}\sqrt{a^7}

    c)
    381\sqrt{{^3}\sqrt{81}}

    d)
    (43y)(33y) (4 {^3}\sqrt{y} )(3 {^3}\sqrt{y} )

    e)
    (43y4)3( {^4}\sqrt{3y-4} {)^{-3}}

    f)
    5(x)3 - {^5}\sqrt{(-x{)^3}}


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