Question

Is 3^20 times 2^14 a factor of 3^22 Times 2^12

Answer 1

no

Explanation:

In order for one number (A) to be a factor of another (B), the exponents of the primes in the prime factorization of A cannot exceed those of the prime factorization of B.

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A = 2^14 × 3^20

B = 2^12 × 3^22

The exponent of the factor 2 in A is 14, which exceeds the exponent of the factor 2 in B (12). Therefore, A cannot be a factor of B.

(3^20)(2^14) is not a factor of (3^22)(2^12)