Exponents are used to avoid the repetition of writing the same numerical values many times.
Write each number in exponent form :
Example 1 :
2 × 2 × 3 × 3 × 3
Solution :
2 × 2 × 3 × 3 × 3
2 is repeated 2 times and 3 is repeated 3 times.
= 22 × 33
Example 2 :
2 × 5 × 5
Solution :
2 × 5 × 5
2 is repeated once and 5 is repeated 2 times.
= 2 × 52
Example 3 :
2 × 3 × 3 × 3 × 5
Solution :
2 × 3 × 3 × 3 × 5
2 and 5 are repeated once and 3 is repeated 3 times.
= 2 × 33 × 5
Example 4 :
5 × 5 × 7 × 7
Solution :
5 × 5 × 7 × 7
5 is repeated twice and 7 is repeated twice.
= 52 × 72
Example 5 :
2 × 2 × 5 × 5 × 5 × 7
Solution :
2 × 2 × 5 × 5 × 5 × 7
2 is repeated twice, 5 is repeated 3 times and 7 is repeated once.
= 22 × 53 × 7
Example 6 :
3 × 3 × 7 × 7 × 11 × 11
Solution :
3 × 3 × 7 × 7 × 11 × 11
3, 7 and 11 are repeated twice.
= 32 × 72 × 112
Example 7 :
56
Solution :
Since 56 is a composite number, we can decompose it into prime factors.
Prime factorization of 56 :
56 = 2 x 2 x 2 x 7
2 is repeated 3 times and 7 is repeated once.
= 23 x 7
Example 8 :
24
Solution :
By decomposing 24 as prime factors, we get
Prime factorization of 24 :
24 = 2 x 2 x 2 x 3
2 is repeated 3 times and 3 is repeated once.
= 23 x 3
Example 9 :
108
Solution :
By decomposing 108 as prime factors, we get
Prime factorization of 108 :
108 = 2 x 2 x 3 x 3 x 3
2 is repeated 2 times and 3 is repeated 3 times.
= 22 x 33
Example 10 :
80
Solution :
By decomposing 80 as prime factors, we get
Prime factorization of 80 :
80 = 2 x 2 x 2 x 2 x 5
2 is repeated 4 times and 5 is repeated once.
= 24 x 5
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