How do you simplify $(6^3)^4 / 12^6$ ?

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Answer 1 · 2017-06-09T09:27:15

$3^6$

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Raising a power to a power, multiply the indices:

$(6^3)^4/(12^6) = 6^12/12^6$

Write the bases as the product of prime factors:

$6^12/12^6 = (2xx3)^12/(2^2xx3)^6$

Raising a power to a power, multiply the indices:

$=(2^12 xx3^12)/(2^12 xx 3^6)$

Subtract the indices of like bases:

$=(cancel(2^12) xx3^12)/(cancel(2^12) xx 3^6) = 3^6$

How do you simplify (6^3)^4 / 12^6(6^3)^4 / 12^6?