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

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Answer 1 · 2018-04-21T00:33:19

$5^(3/4)$

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

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

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

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

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

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

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

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

$=> 5^(3/4)$

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