Question

How can you express the number 104 as a power as a product of the same factor?

a) 2^2 * 13
b) 4^2 * 13
c) 2^3 * 13
d) 4^3 * 13

Answer 1

To express the number 104 as a product of the same factor, factorize it by repeatedly dividing by 2, ending with three 2s and the prime number 13, resulting in the expression 2³ × 13.

The correct option is c.

Step-by-step explanation:

To answer the question on how you can express the number 104 as a power as a product of the same factor, we must factorize the number 104. Firstly, recognize that 104 is an even number and can thus be divided by 2. The factorization process would look like this:

1. Divide 104 by 2: 104 ÷ 2 = 52.
2. Recognize that 52 is also divisible by 2: 52 ÷ 2 = 26.
3. Again, 26 is divisible by 2: 26 ÷ 2 = 13.
4. Since 13 is a prime number, we stop our factorization here.

We ended up dividing by 2 three times, so we have three 2s. Therefore, 104 expressed as a power as a product of the same factor is 2 raised to the power of 3 times 13, or 2³ × 13, which is option (c).

The correct option is c.

Answer 2

The number 104 can be expressed as a power as the product of the same factor 2³ × 13, which is option (c).

Step-by-step explanation:

To express the number 104 as the power of a product of the same factor, we look for prime factors. First, we see that 104 is an even number, so it is divisible by 2. We divide 104 by 2 to get 52, which further indicates that 104 is 2² × 26. Continuing this process, we divide 26 by 2 to get 13, which is a prime number. Therefore, 104 can be written as 2³ × 13, which is option (c).