EXPRESS PRODUCT OF PRIME NUMBERS IN INDEX FORM

Write each number in index form :

Problem 1 :

2×2×3×3x3

Solution :

= 2×2×3×3×3

Here, 2 is repeated 2 times and 3 is repeated 3 times.

So the exponential form is 2² × 3³.

Problem 2 :

2×5×5

Solution :

= 2×5×5

Here, 2 is repeated once and 5 is repeated 2 times.

So the exponential form is 2¹ × 5².

Problem 3 :

2×3×3×3×5

Solution :

= 2×3×3×3×5

Here 2 and 5 are repeated once and 3 is repeated 3 times.

So the exponential form is 2¹ × 3³ × 5¹.

Problem 4 :

5×5×7×7

Solution :

= 5×5×7×7

5 is repeated 2 times and 7 is repeated 2 times.

So the exponential form is 5² × 7².

Problem 5 :

2 × 2 × 5 × 5 × 5 × 7

Solution :

= 2 × 2 × 5 × 5 × 5 × 7

2 is repeated 2 times, and 5 is repeated 3 times and 7 is repeated once.

So the exponential form is 2² × 5³ × 7¹.

Problem 6 :

3×3×7×7×11×11

Solution :

= 3×3×7×7×11×11

Here 3, 7 and 11 is repeated 2 times.

So the exponential form is 3² × 7² × 11².

Problem 7 :

2×2×2×3×3×3×3

Solution :

= 2×2×2×3×3×3×3

2 is repeated 3 times, and 3 is repeated 4 times.

So the exponential form is 2³ × 3⁴.

Problem 8 :

5×5×5×5×5×5×7×7×7

Solution :

= 5×5×5×5×5×5×7×7×7

5 is repeated 6 times, and 7 is repeated 3 times.

So the exponential form is 5⁶ × 7³.

How to Express a Number as the Product of its Prime Factors

Write the following in exponent form :

Problem 1 :

25

Solution :

= 25

= 5×5

Here 5 is repeated 2 times.

So, the exponential form is 5².

Problem 2 :

36

Solution :

= 36

= 6×6

6 is repeated 2 times.

So, the exponential form is 6².

Problem 3 :

125

Solution :

125 = 5×5×5 5 is repeated 3 times. So, the exponential form is 53.

Problem 4 :

343

Solution :

343 = 7 × 7 × 7 Here, 7 is repeated 3 times So, the exponential form is 73.

Write the following in exponent form with 3 as a base :

Problem 1 :

3

Solution :

Since, 3 is in the base, we don’t have any power for 3,

So, consider 3¹.

So the exponential form is 3¹.

Problem 2 :

27

Solution :

27 = 3 × 3 × 3 Since, 3 is repeated 3 times So the exponential form is 33.

Problem 3 :

81

Solution :

= 3 × 3 × 3 × 3 = 34   Since, 3 is repeated 4 times So the exponential form is 34.

Problem 4 :

729

Solution :

= 3 × 3 × 3 × 3 × 3 × 3 = 36   Here, 3 is repeated 6 times So the exponential form is 36.