# Math՚s: Exponential Notation: Exponential Form and Prime Factorization (For CBSE, ICSE, IAS, NET, NRA 2022)

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## Exponential Notation

• The notation for writing the product of a number by itself a number of times is called the Exponential Notation or Exponential Form.
• For Ex- When 3 is multiplied 4 times by itself i.e.. is written in exponential notation as and is read as raised to the power .
• Base- The number which is being multiplied is known as the base.
• Exponent- The number of times the base is getting multiplied by itself, is known as the power.

In the above example, 3 is the base whereas 4 is the exponent.

## Prime Factorization

• Expressing a composite number as a product of its prime factors is known as prime factorization.
• Sometimes, for writing a big number in exponential form, we do prime factorization. For Ex- Write in exponential form
• Do prime factorization of as follows:
 2 16900 2 8450 5 4225 5 845 13 169 13 13 1

Write the product of prime factors in exponential form-

1. Write the following in exponential form and state the base and exponent in each case.

(i)

(ii)

(iii)

(iv)

Solution: (i)

Base- ; Exponent-

(ii)

Base- ; Exponent-

(iii)

Base-; Exponent-

(iv)

Base- ; Exponent-

2. Simplify the following:

(i)

(ii)

Solution: (i)

(ii)

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