Convert between radicals and rational exponents

Lessons

• Introduction
  a)

  How to convert between radicals and rational exponents?
  
  

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• 1.
  Write the following in the radical form
  a)

  ${27^{- \frac{2}{3}}}$
  
  
  
  b)

  $(-8 {)^{- \frac{3}{5}}}$
  
  
  

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• 2.
  Write the answer with positive exponents and then as entire radical
  a)

  $( \frac{9}{4}{)^{- \frac{3}{4}}}$
  
  
  
  b)

  $-(-16 {)^{- \frac{4}{5}}}$
  
  
  
  c)

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

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• 3.
  Write the answer as a power and evaluate
  a)

  ${^5}\sqrt{a^3}$
  
  
  
  b)

  $1/ {^4}\sqrt{a^7}$
  
  
  
  c)

  $\sqrt{{^3}\sqrt{81}}$
  
  
  
  d)

  $(4 {^3}\sqrt{y} )(3 {^3}\sqrt{y} )$
  
  
  
  e)

  $( {^4}\sqrt{3y-4} {)^{-3}}$
  
  
  
  f)

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

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