Question

Determine the prime factorization of 88.
a. 22 • 11
b. 22 • 3 • 5
c. 23 • 11
d. 2 • 32 • 5

Answer 1

None of the answers above are the prime factorization of 88
Each one of them is way too big.

88 can be broken down in 11 x 8
While 11 is prime,  8 is still composite and can be broken down into 2 x 4
The 2 is prime but the 4 is still composite so it can be broken down into 2 x 2, both of which are prime.  So it appears we have (in numerical order smallest to biggest):
2 x 2 x 2 x 11  or    2³  x 11   this is the correct prime factorization of 88.

Check:  2 x 2 x 2 = 8 x 11 = 88

Answer 2

The Prime Factors of 88 are:
2 x 2 x 2 x 11

In Exponential Form:
2₃ x 11₁

Prime Factors Tree:
     88               
     /  \               
2         44          
          /  \          
     2         22     
               /  \     
          2         11

Hopefully you understand now! :D