Exponents: Rational exponents

Lessons

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

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• 2.
  Simplifying Expressions Using: ${^n}\sqrt{x}=x^{\frac{1}{n}}$
  Simplify the following expressions if possible.
  a)

  $64^{\frac{1}{3}}$
  $16^{\frac{1}{4}}$
  
  
  b)

  $(-16)^{\frac{1}{4}}$
  $(-32)^{\frac{1}{5}}$
  
  

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• 3.
  evaluate:
  a)

  $(8)^{5 \over 3}$
  
  
  b)

  $(-{243 \over 32})^{-{2 \over 5}}$
  
  

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

  $27^{-\frac{1}{3}}$
  
  
  b)

  $\frac{1}{{^6}\sqrt{x}}$
  
  
  c)

  $(64x^8)^{-\frac{1}{2}}$
  
  

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

  ${^2}\sqrt{x^6}$
  
  
  b)

  $25^{\frac{3}{2}}$
  
  
  c)

  $(-125)^{-\frac{2}{3}}$
  
  
  d)

  $\sqrt{36x^{16}y^{24}}$
  
  
  e)

  ${^3}\sqrt{-216a^9b^{24}c^{117}}$
  
  

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