Question

Expresa en forma de una sola potencia

Answer 1

$a) ( \frac{x}{2} )^{1/3} * ( \frac{x}{2} )^{3/5} = ( \frac{x}{2} )^{3/5} = ( \frac{x}{2})^{1/5}$

$b) ( \frac{- 3}{4} )^{4} * ( \frac{-3}{4} )^{-2/5} * ( \frac{-3}{4} ) = (\frac{-3}{4})^{23/5}$

$c) [(1 + \sqrt{2})^{3} ]^{3/5} / (1 + \sqrt{2})^{-1/2} = (1 + \sqrt{2} )^{3*3/5} / (1 + \sqrt{2})^{-1/2} =$
$(1 + \sqrt{2})^{9/5} / (1 + \sqrt{2})^{-1/2} = (1 + \sqrt{2}) x^{9/5 - (-1/2)} = (1 + \sqrt{2})^{23/10}$

$d) ( \frac{-1}{5})^{-7} / ( \frac{-1}{5})^{-7} = ( \frac{-1}{5} )^{-7-(-7)} =( \frac{-1}{5})^{0}$