Express the prime factorization of 128 as a product of prime numbers with exponents
Express the prime factorization of 54 as a product of prime numbers with exponents
To express the prime factorization of 128 as a product of prime numbers with exponents, we need to break down 128 into its prime factors.
Step 1: Find a prime number that divides 128. The smallest prime number is 2.
Step 2: Divide 128 by 2. Since 128 is even and divisible by 2, the quotient is 64.
Step 3: Repeat step 2 with the quotient. Divide 64 by 2, getting a quotient of 32.
Step 4: Again, divide 32 by 2, resulting in a quotient of 16.
Step 5: Continue dividing by 2 until the quotient is not divisible by 2 anymore. Divide 16 by 2, 8, 4, and 2, in that order. The final quotient will be 1.
Putting it all together, the division steps are:
128 ÷ 2 = 64
64 ÷ 2 = 32
32 ÷ 2 = 16
16 ÷ 2 = 8
8 ÷ 2 = 4
4 ÷ 2 = 2
2 ÷ 2 = 1
Since we divided by 2 seven times, we can express the prime factorization of 128 as:
2^7
Therefore, the prime factorization of 128 as a product of prime numbers with exponents is 2^7.