# Math's: Exponential Notation: Exponential Form and Prime Factorization

Doorsteptutor material for IEO Class-2 is prepared by world's top subject experts: Get full length tests using official NTA interface: all topics with exact weightage, real exam experience, detailed analytics, comparison and rankings, & questions with full solutions.

Download PDF of This Page (Size: 128K) ↧

## 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)