Convert between radicals and rational exponents

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  1. How to convert between radicals and rational exponents?
  1. Write the following in the radical form
    1. 2723 {27^{- \frac{2}{3}}}
    2. (8)35(-8 {)^{- \frac{3}{5}}}
  2. Write the answer with positive exponents and then as entire radical
    1. (94)34( \frac{9}{4}{)^{- \frac{3}{4}}}
    2. (16)45 -(-16 {)^{- \frac{4}{5}}}
    3. (5x37)(25x37) \frac{(5 {x^\frac{3}{7}} )}{(25 {x^{- \frac{3}{7}})}}
  3. Write the answer as a power and evaluate
    1. 5a3{^5}\sqrt{a^3}
    2. 1/4a7 1/ {^4}\sqrt{a^7}
    3. 381\sqrt{{^3}\sqrt{81}}
    4. (43y)(33y) (4 {^3}\sqrt{y} )(3 {^3}\sqrt{y} )
    5. (43y4)3( {^4}\sqrt{3y-4} {)^{-3}}
    6. 5(x)3 - {^5}\sqrt{(-x{)^3}}
Topic Notes
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.
Ax/y=yAx {A^{x/y}} = {^y}\sqrt{A^x}