 # Exponents and Powers Class 7 Notes: Chapter 13

Exponents and powers for class 7 is one of the most crucial chapters and introduces a variety of important concepts which form the foundation of various higher level concepts. The CBSE class 7 notes for chapter 13 i.e. exponents and powers can help students to learn the concepts easily and revise them quickly.

Key points highlighted in exponents and powers class 7 notes are:

• Meaning of Exponents and Powers
• Laws of Exponents
• Expressing Large Numbers in the Standard Form
• Example Questions
• Practice Questions

## What are exponents and Powers?

Exponents can be defined as a quantity which describes the power to which a particular base number is raised to. On the other hand, power simply implies the number of time the same base number has to be multiplied. Learn more about exponents and powers from this article along with examples.

Expressing Exponents:

Any number “a” which is raised to the power of “n” can be expressed as-

$a^{n}=a\times a\times a \times a \times ….a (n \;times)$

Example of Exponents:

For any number, suppose,

$5^{3}$

Here, 5 is the base number and 3 is the exponent. The solution to it will be 5 × 5 × 5 = 15.

### Laws of Exponents

There are certain laws which all the numbers in their exponential form obey. There are 7 main laws of exponents which are discussed below. In these laws, the base numbers “a” and “b” are considered which are non-zero and the exponents “m” and “n” are taken which are whole numbers.

• Law 1: $a^{m}\times a^{n}=a^{m+n}$
• Law 2: $a^{m}\div a^{n}=a^{m-n}\; for\; m>n$
• Law 3: $(a^{m})^{n}$
• Law 4: $a^{m}\times b^{m}=(ab)^{m}$
• Law 5: $a^{m}\div b^{m}=(\frac{a}{b})^{m}$
• Law 6: $a^{0}=1$
• Law 7: $(-1)^{even\; number}=1, \; and, (-1)^{odd\; number}=-1$

### Expressing Large Numbers in the Standard Form

Large numbers can be expressed using exponents and make them convenient to read and write. To express any large number, first, the base number is converted to its standard form (i.e. expressed as decimals). An example is given below for better understanding.

Example: The standard form of 5985 will be-

5985=5.985 × 103

Similarly, 45634 = 4.5634 × 104

For expressing large quantities, like the mass of Uranus, exponents can be used for convenience.

Mass of uranus = 86,800,000,000,000,000,000,000,000 kg

It can be written using exponents as-

Mass of Uranus = 8.68 × 1025 Kg

### Example Questions

Example 1:

Simplify: 23 × a3 × 5a4

Solution:

23 × a3 × 5a4 = 23 × a3 × 5 × a4

= 23 × 5 × a3 × a4 = 40 a7

Example 2:

Expand: $(\frac{-7}{4})^{6}$

Solution:

$(\frac{-7}{4})^{6} = \frac{-7^{6}}{4^{6}}=\frac{(-7)\times (-7)\times(-7)\times(-7)\times(-7)\times(-7)}{4\times 4\times 4\times 4\times 4\times 4}$

### Practice Questions

1. Simplify the following:
1. $\frac{\left ( 2^{5} \right )^{2}\times 7^{3}}{8^{3}\times 7}$
2. $\frac{25\times 5^{2}\times t^{8}}{10^{3}\times t^{4}}$
3. $\frac{3^{5}\times 10^{5}\times 25}{5^{7}\times 6^{5}}$
1. Express the following expanded forms to their actual base forms
1. $8\times 10^{4}+6\times 10^{3}+0\times 10^{2}+4\times 10^{1}+5\times 10^{0}$
2. $4\times 10^{5}+5\times 10^{3}+3\times 10^{2}+2\times 10^{0}$
3. $3\times 10^{4}+7\times 10^{2}+5\times 10^{0}$
4. $9\times 10^{5}+2\times 10^{2}+3\times 10^{1}$
1. Express the following to their expanded forms
1. 279404
2. 3006194
3. 2806196
4. 120719