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
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
The prime factorization in exponent form of 27 is: 33 = 27
24
Prime factorization of 160 in exponential form is 25 x 5.
32 = 25
It is: 72 = 49
There are no exponents needed. The prime factorization of 55 is: 5 x 11
Prime factors in exponent form: 2^2 * 17
Prime factors in exponent form: 5^2 * 13
302 = 21 * 1511
71 x 311
22*32 = 36
45 = 32*5