Sometimes prime factorizations have repeated factors. It is often easier to write them with exponents.
2 x 2 x 2 x 3 x 3 x 3 = 216
2^3 x 3^3 = 216
When prime factors are repeated, it saves space to use exponents.
2 x 2 x 2 x 3 x 3 x 3 = 216
2^3 x 3^3 = 216
It's a short way to count the repeated factors.
2 x 2 x 2 x 3 x 3 = 72
2^3 x 3^2 = 72
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23 x 52 = 200
It is: 2*3*17 =102 and exponents not needed
28 = 22 x 71
2 x 3 x 5 x 19 No exponents required.
Think of the "ex" in index as meaning exponent. Write the prime factorization with exponents. 216 = 23 x 33