How do you simplify #125^(2/9) * 125^(1/9) / 5^(1/4)#?

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Answer 1 · 2018-04-21T00:33:19

#5^(3/4)#

#=> 125^(2/9) cdot (125^(1/9))/5^(1/4)#

#=> 5^(3 × 2/9) cdot (5^(3 × 1/9))/5^(1/4) color(white)(...)[∵ 125 = 5^3]#

#=> 5^(2/3) cdot 5^(1/3) / 5^(1/4)#

#=> (5^(2/3 + 1/3))/5^(1/4) color(white)(...)[∵ a^x a^y = a^(x + y)]#

#=> 5^(3/3) / 5^(1/4)#

#=> 5 / 5^(1/4)#

#=> 5 cdot 5^(-1/4) color(white)(...)[∵ 1/a^x = a^(-x)]#

#=> 5^(1 - 1/4)#

#=> 5^(3/4)#