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

Doorsteptutor material for CBSE/Class-10 is prepared by world's top subject experts: get questions, notes, tests, video lectures and more- for all subjects of CBSE/Class-10.

## 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)