## 1. Exponents and Powers

- Books Name
- class 7 Mathematics Book

- Publication
- ReginaTagebücher

- Course
- CBSE Class 7

- Subject
- Mathmatics

**Chapter – 13**

**Exponents and Powers**

Power is the product of multiplying a number by itself. It shows how many times the base is multiplied by itself.

The base number tells what number is being multiplied.

The exponent, a small number written above and to the right of the base number, tells how many times the base number is being multiplied.

The number 5 is called the base, and the number 2 is called the exponent.

An **exponent** is a small number written above and to the right of the base number, tells how many times the base number is being multiplied.

The base **a** raised to the power of **n **is equal to the multiplication of **a, n** times:

a⋅a⋅a⋅...⋅a** = **an

a is the base and n is the exponent.

For example, **“3 to the power 4”** may be written as 34. Here, the base number is 3, and the exponent is 4. It means that 3 is being multiplied by itself 4 times: 3 x 3 x 3 x 3.

Where,

3 x 3 x 3 x 3 = 81 or 34 **= **81.

The positive value of a positive integer is always positive.

A negative number is positive if the multiplier is an even number and negative if the multiplier is an odd number.

- 'a' square or 'a' in the second stage:

a^{2}=a⋅ a

- 'a' cube or 'a' in the third stage:

a^{3}= a⋅ a⋅ a

- 'a' in the fourth stage:

a^{4 }= a⋅ a⋅ a⋅ a

A fraction with a whole negative multiplier is taken to be a fraction with a numerator of 1, but the denominator is the same base with the opposite positive multiplier.

a−n=1an (n−naturalnumbers)

an⋅am=an + m;an:am = an−m,n> m,a ≠ 0;(an)m=an⋅m

Where n and m are integers.

The normal form of a number is called the multiple of this number: a⋅10nwhere1 ≤ a < 10

Note that greater than 1 and less than 10.

When dividing degrees with the same base, the powers are subtracted, and the base remains unchanged.

** an:am=an−m**

**Where a≠0, n and m are natural numbers such that n>m.**

## 2. Laws of exponents

- Books Name
- CBSE Class 7 Mathematics Book

- Publication
- Param Publication

- Course
- CBSE Class 7

- Subject
- Mathmatics

**Base and Exponent**

If a is a non-zero rational number and n is a natural number, then the product a × a × a × ... up to n times is denoted by a^{n} and is read as 'a raised to the power n'. Rational number 'a' is called the base and natural number ‘n’ is known as the exponent. Also, a^{n} is known as the exponential form of

a × a × a × ... up to n times.

For any non-zero rational number, we have :

a^{0} = 1 and a^{1} = a.

## 3. Miscellaneous examples using the laws of exponents

- Books Name
- CBSE Class 7 Mathematics Book

- Publication
- Param Publication

- Course
- CBSE Class 7

- Subject
- Mathmatics

**Laws of exponents**

If a and b are non-zero rational numbers and m and n are natural numbers, then following are the laws of exponents :