Question 548109
{{{ ( 8^(2/3) * 27^(3/2) ) / ( 16^(3/4) * 9^(3/4) ) }}}
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Recall.
{{{ x^a * y^b = x*y^(a+b) }}}
{{{ x^a / y^b = (x/y)^(a-b) }}}
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We also can apply what we know about the distributive property and fraction.
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{{{ ( 8^(2/3) * 27^(3/2) ) / ( 16^(3/4) * 9^(3/4) ) = (8^(2/3) / 16^(3/4)) * (27^(3/2) / 9^(3/4)) = ((1/2)^(2/3-3/4) ) * ( 3^(3/2-3/4) ) }}}
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{{{  ((1/2)^(2/3-3/4) ) * ( (3)^(3/2-3/4) ) = (1/2)^(8/12-9/12) * (3)^(6/4-3/4) = (1/2)^(-1/12)*(3)^(3/4) }}}
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{{{ (1/2)^(-1/12)*(3)^(3/4) = (3/2)^(-1/12+3/4) = (3/2)^(8/12) = (3/2)^(2/3) }}}