How do you simplify $(6^(1/2) * 6^(3/2))^ (4/3)$ ?

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Answer 1 · 2015-06-05T20:28:06

$(6^(1/2)*6^(3/2))^(4/3)=(6^(1/2+3/2))^(4/3)$

$=(6^2)^(4/3)=6^(2*4/3)$

$=6^(8/3)$

...using the properties of exponentials:

$a^b*a^c = a^(b+c)$

$(a^b)^c = a^(bc)$

How do you simplify (6^(1/2) * 6^(3/2))^ (4/3)(6^(1/2) * 6^(3/2))^ (4/3)?