The numbers 756 and 72, expressed as products of prime factors, are 756 = 2² x 3³ x 7 and 72 = 2³ x 3²

Use these result to find,

the smallest integer, x, such that 756x is a perfect cube.

Thanks you

Hi Yvonne,

8 = 2^{3}, 27 = 3^{3}, 216 = 2^{3} × 3^{3} = 6^{3}, 64 = 2^{6} = 4^{3} are all cubes. For n to be a cube it must be that the powers of the primes in the prime factor decomposition of n must be divisible by 3.

Penny

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