The following Topics and Sub-Topics are covered in this chapter and are available on MSVgo:

Exponents and Powers is an important NCERT maths chapter that explains the basics of exponential functions and their importance. You must have learned the concept of exponents and power in your basic algebra class, where you use powers over variables. For example, to simplify (a + b)2 = a2 + 2ab + b2.

The general form of exponents is written as (a)n, where a and n are any unique natural numbers.

The expanding of (a)n = a x a x a x a x a x a x……..n times.

For example, (2)4 = 2 x 2 x 2 x 2 = 16

The (a)n is the shorthand notation of a very large number that has been written in a simple form.

Let’s check some basic laws of exponents that apply to the exponent and power numbers.

**Multiplication Law:**When we multiply powers with the same base, we need to add the different powers of the base. This can be depicted mathematically as:- (a)m x (a)n = (a)(m+n)
- Where a, m, and n are natural numbers.
**Division Law:**When we divide powers with the same base, we need to subtract the denominator’s base power from the numerator’s base. This can be depicted mathematically as:- am ÷ an = am / an = a(m-n)
- Where a, m, and n are any natural numbers.
**Negative Exponent Law:**It is represented as:- a(-m)= 1/(a)m
- Where a and m are any integer.

Apart from these three basic laws, we have some exponent and power rules that come into play. We will check them below.

**Rule 1:**a0 = 1. This rule is a basic hypothesis that can be proved by using the division law discussed above.**Rule 2:**((a)m)n = (a)(m x n). Multiplying powers with the same exponents, we get an equivalent exponent to multiplicate individual powers. We can also call it taking the power of a power.**Rule 3:**am/bm = (a/b)m. Dividing powers with the same exponents. When we have a division with the same exponents and same base, we can simplify it, as shown in the rule above.**Rule 4:**am × bm = (ab)m. When we multiplicate with the same exponents and the same base, we can simplify it, as shown in the rule above.

Numbers and exponents are the basics of mathematics and are used to depict nature’s physical quantities. There are many usages of exponents and powers in different fields and industries. Some of them are given below.

- They are used extensively in the decimal number system to depict a scientific notation of large numbers.
- They are also used in Physics to solve formulas and derive their proofs.
- They have importance in Chemistry to note the reaction time of any chemical reaction.
- Moreover, they find application in Geometrical Algebra and Coordinate System.

Exponents and powers are an important mathematical topic used extensively in both maths and science. You must have started learning them in the algebra section and while solving proofs in the physics section. Apart from this, they are also used in chemistry and computer science. There are some simple rules and laws associated with exponents and powers that simplify their use. The rules and laws are discussed above in detail.

**What are exponents and powers?****What is the power of a power rule for exponents?****What are the five rules of exponents?****How do you teach exponents and powers?****How do you calculate exponential powers?****What are the rules of exponents?**

**Multiplication Law:**When we multiply powers with the same base, we need to add the different powers of the base numbers. This can be depicted mathematically as:(a)m x (a)n = (a)(m+n)- Where a, m, and n are natural numbers.
**Division Law:**When we divide powers with the same base, we need to subtract the denominator’s base power from the numerator’s base. This can be depicted mathematically as:- am ÷ an = am / an = a(m-n)
- Where a, m, and n are any natural numbers.
**Negative Exponent Law**: It is represented as:- a(-m) = 1/(a)m
- Where a and m are any integer.