# EXPRESS PRODUCT OF PRIME NUMBERS IN INDEX FORM

What is index form ?

When a number is expressed with exponents, or one number to a power of another, it is considered to be in index form.

To write the the given product of prime factors in index form, we will follow the steps given below.

Step 1 :

Observe the terms and count it how many times they are repeated.

Step 2 :

The term which is repeated should be written in the base and the number of times repeated should be in the power.

Note :

If we see the term once, the power should be considered as 1.

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 = 5×5×55 is repeated 3 times.So, the exponential form is 53.

Problem 4 :

343

Solution :

 343 = 7 × 7 × 7Here, 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 × 3Since, 3 is repeated 3 timesSo 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.

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