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#