Question

find the smallest number in which 64a^5 should be divided so that the quotient is perfect cube

Answer 1

by prime factorisation
64a^5. can be write as 2×2×2×2×2×2×a×a×a×a×a
we have to make these no.s in pair of 3 (because we have to know about cube) and we have to count it only one time
2×2×a ×3√a×a
a×a means a^2 is not in pair of 3
so the smallest no. in which 64a^5 should be divided so that the quotient is perfect cube is a^2 or we can say it a×a