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Question
Rewrite with rational exponents:
(sqrt5mn)^7
is the answer 5mn^7
The answer to (sqrt5mn)^7 is √(5mn)^7 = 5³m³n³√(5mn) = 125m³n³√(5mn)
since the powers beneath a squareroot can be divided by 2 and taken outside.
Since they are odd, a power of 1 is left inside.
As another example, if we have √512, that would be √2^9 = (√2^8)√2.
8/2 is 4, so the answer is (2^4)√2 = 16√2.
Now if we look at the problem another way, it is the same as √256√2.
It is known that 256 = 16², so that is the same as 16√2.
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Scott A Wilson
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