Express the prime factorization of 128 as a product of prime numbers with exponents.(1 point)
128 = 2^7
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To express the prime factorization of 128, we need to find its prime factors. The prime factors are the prime numbers that divide 128 without leaving a remainder.
To find the prime factors of 128, we start by dividing it by the smallest prime number, which is 2. If 2 divides evenly, we continue dividing the quotient by 2 until we can no longer divide evenly. Let's go step by step:
128 ÷ 2 = 64
64 ÷ 2 = 32
32 ÷ 2 = 16
16 ÷ 2 = 8
8 ÷ 2 = 4
4 ÷ 2 = 2
Now, we are left with 2. We can see that 2 cannot be divided any further. Therefore, the prime factors of 128 are 2 multiplied by itself 7 times:
128 = 2 × 2 × 2 × 2 × 2 × 2 × 2
Alternatively, we can write it using exponents:
128 = 2^7
So, the prime factorization of 128 as a product of prime numbers with exponents is 2^7.