Express in index notation, 8960 as a product of its prime numbers.

Answer 1

To express 8960 as a product of its prime numbers in index notation, we need to determine its prime factors.

First, we can check if 2 is a factor of 8960. Since 8960 is an even number (ends in 0), we know that it is divisible by 2.

Dividing 8960 by 2, we get 4480.

Next, we check if 2 is still a factor of 4480.

Dividing 4480 by 2, we get 2240.

Continuing this process, we find that 2 is a factor of 8960 four times (2 x 2 x 2 x 2 = 16).

Next, we need to check the next prime number, 3.

Dividing 2240 by 3 is not possible without any remainder. Thus, 3 is not a factor of 8960.

Then, we can check the next prime number, 5.

Dividing 2240 by 5 gives us 448.

Further, dividing 448 by 5 gives us 89.6. However, 89.6 is not divisible by 5 as it has a decimal portion.

Therefore, 5 is not a factor of 8960.

Next, we can check the prime number 7.

Dividing 2240 by 7, we get 320.

Then, dividing 320 by 7 gives us 45.7142. However, 45.7142 is not divisible by 7 as it has a decimal portion.

Therefore, 7 is not a factor of 8960.

Lastly, we check the prime number 11.

Dividing 2240 by 11, we get 203.6363. However, 203.6363 is not divisible by 11 as it has a decimal portion.

Therefore, 11 is not a factor of 8960.

To express 8960 as a product of its prime numbers in index notation, we have:

8960 = 2^4 x 5^0 x 7^0 x 11^0

So, in index notation, 8960 is written as:

8960 = 2^4