Quote:
Originally Posted by chriscurtis
2^2 = 4
((2^2)^4)= 4^4 = 16
((2^2)^2)^2 = 256
etc
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4^4 is 256, not 16. 2^4 is 16.
Quote:
Originally Posted by chriscurtis
exponents of exponents are not the same as exponents
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Oh? How are they different?
Exponentiation with integers is just a convenient way of expressing repeated multiplication.
a^b = a*a...*a, b times.
(a^b)^c = (a*a...*a)*(a*a...*a)*...(a*a...*a), c times.
Since multiplication is associative, x*(y*z) = x*y*z, so:
(a^b)^c = a*a...*a, b*c times. So,
(a^b)^c = a^(b*c)