SOLUTION: I was just wondering what the best way to solve this problem would be: 16/8^4 The way I solved it was that I multiplied out 8^4 and got 4069. Then I simplified to get my ans

Algebra ->  Algebra  -> Exponents-negative-and-fractional -> SOLUTION: I was just wondering what the best way to solve this problem would be: 16/8^4 The way I solved it was that I multiplied out 8^4 and got 4069. Then I simplified to get my ans      Log On

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Question 25748: I was just wondering what the best way to solve this problem would be:
16/8^4
The way I solved it was that I multiplied out 8^4 and got 4069. Then I simplified to get my answer of 1/256. Is there a shorter way to get the solution?
Thank you.
Answer by josmiceli(6797) About Me  (Show Source):
You can put this solution on YOUR website!
There is another way to approach it.
16 = 2^4
Rewrite the problem as:
2^4/8^4
This is the same as
(2/8)^4
why?
look at this one:
a^4/b^4 = (a x a x a x a) / (b x b x b x b)
what's this:
(a/b)^4
(a/b)* (a/b) * (a/b) * (a/b)
it's also (a x a x a x a) / (b x b x b x b)
so, (2/8)^4 = (1/4)^4 = 1/256