Maths-
General
Easy

Question

Which expression is equivalent to g to the power of 4 over 5 end exponent h to the power of 2 over 5 end exponent, where g and h are positive?

  1. fourth root of g to the power of 5 h to the power of 10 end root
  2. fifth root of g to the power of 4 h squared end root
  3. fraction numerator 1 over denominator fourth root of g to the power of 5 h to the power of 10 end root end fraction
  4. fraction numerator 1 over denominator fifth root of g to the power of 4 h squared end root end fraction

The correct answer is: fifth root of g to the power of 4 h squared end root


    HINT : Rearrange the exponential form
    table attributes columnalign right left right left right left right left right left right left columnspacing 0em 2em 0em 2em 0em 2em 0em 2em 0em 2em 0em end attributes row cell open g to the power of 4 over 5 end exponent h to the power of 2 over 5 end exponent equals open parentheses g to the power of 4 space cross times space h squared close parentheses to the power of 1 divided by 5 end exponent text  {Reason  end text a to the power of n b to the power of p n end exponent equals open parentheses a b to the power of p close parentheses to the power of n close curly brackets end cell row cell open parentheses g to the power of 4 space cross times space h squared close parentheses to the power of 1 divided by 5 end exponent equals fifth root of g to the power of 4 h squared end root open square brackets text  Reason  end text a to the power of 1 over n end exponent equals n-th root of a close square brackets end cell end table

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