WRITE THE PRODUCT IN EXPONENTIAL FORM

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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