how can the whole number 378 be expressed as a product of prime numbers with exponents

Answer 1

To express 378 as a product of prime numbers with exponents, we need to find its prime factorization.

Start by dividing 378 by the smallest prime number, which is 2.
378 ÷ 2 = 189

Now, divide 189 by 2 again.
189 ÷ 2 = 94.5

Since 94.5 is not a whole number, we move on to the next prime number, which is 3.
189 ÷ 3 = 63

Continuing with the next prime number, divide 63 by 3.
63 ÷ 3 = 21

The next prime number is 5, so divide 21 by 5.
21 ÷ 5 = 4.2

Since 4.2 is not a whole number, we move on to the next prime number, which is 7.
21 ÷ 7 = 3

Now, we cannot divide further because 3 is a prime number itself.

By multiplying all the divisors 2, 2, 3, 3, 7, and 3 together, we get the prime factorization of 378:
2 × 2 × 3 × 3 × 7 × 3 = 2^2 × 3^2 × 7 × 3 = 2^2 × 3^3 × 7

Therefore, 378 can be expressed as a product of prime numbers with exponents as 2^2 × 3^3 × 7.