Exponents and Powers Class 8 Notes given here are a great study tool to boost productivity and improve overall knowledge about the topics covered in chapter 12. Students can use these notes to have a thorough revision of the entire chapter and at the same be well equipped to write the exam. That being said, some of the important topics discussed in chapter 12 notes include;

- What Are Exponents?
- Powers with Negative Exponents
- Laws of Exponents
- Use of exponents
- Important Questions

## What Are Exponents?

Exponents are numbers which indicate how many times multiplication has to be done to a number to get the desired result. An exponent is a simple but powerful tool and is basically written above the base number on the right side. Usually, an exponent or power can either be positive or negative.

For example, if we take the number 8 we need to multiply 2 three times as in 8 = 2 x 2 x 2. Here, 2 is the base number and 3 is the exponent.

### Powers with Negative Exponents

Negative power is quite similar to the positive power of an exponent. The only difference is that in negative power the value of the expression is the correlative of the value obtained with a positive number. A negative exponent also means how many times to divide by the number.

Example: 8^{-1} = 1 ÷ 8 = 1/8 = 0.125

**Laws of Exponents**

In instances where a and b are non-zero integers while m and n are other integers, then

- a
^{m}xa^{n }= a^{m+n} - a
^{m}/ a^{n }= a^{m-n} - (a
^{m})^{n }= a^{mn} - a
^{m}×b^{m }= (ab)^{m} - a
^{m }/ b^{m }= (a / b)^{m} - a
^{0 }= 1

### Uses of Exponents

- It is used to express small numbers in standard form
- Case 1: Large numbers can be expressed in standard form with the help of positive exponents
- Likewise, small numbers can be expressed using negative exponents

- Exponents can be used in the comparison of very small and very large numbers.

### Examples

### Important Questions

- Get the multiplicative inverse of the following numbers.

(i) 10^{-5} (ii) 5^{-3} (iii) 7^{7-2} (iv) 10^{-1000}

- Simplify and express it in the exponential form.

(i) (–2)^{-3} × (–2)^{-4 }(ii) 3^{2} × 3^{-5} × 3^{6}

- Express 6
^{-3}as a power with the base 3. - There is a stack of 6 coins each of thickness 25 mm and 6 paper notes each of thickness 0.020 mm kept in a table. What is the total thickness of the stack?
- Express the given numbers in the usual form.

(i) 3.52 × 10^{5} (ii) 7.54 × 10^{-4}

**Also Read:**

An Introduction To Exponents | A Key To The Laws Of Exponents |

Laws Of Exponents With Integral Power | Exponents Formula |