find the smallest number by which the following number must be divided to make the quotients perfect cube 54
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Answer:
54 = (2^1)(3^3)
We have to make all powers of the prime factors a multiple of 3 because:
(2^(3a))(3^(3b))
= [(2^a)(3^b)]^3
Which is a perfect cube.
Therefore we have to divide 54 by 2 to make the power of the ‘2’ be 0
So the answer is 2
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