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

You must have come across the use of numbers in the form of **exponents and powers** in various real-life scenarios, such as measuring scales of Ritcher and pH, the demography of a country, and economics. It is an important topic that is applied in Physics, computer games, engineering, accounting, finance, and other vital disciplines. From the examination point of view, you can expect quite a few questions from this chapter. Besides this, you will find its application in other chapters too. We will dive into more details on exponents and powers in the next sections.

We can write big numbers in short form using **exponents and powers**. For example, if we have to write 2 x 2 x 2 x 2 x 2 x 2, then it can be represented in exponential form by raising 2 to the power 6, i.e., 26, where 2 is known as the base, and 6 is known as its power.

Now, let us consider a case of **powers with negative exponents**. If we write 10-3, then it implies 1/103 or 0.001.

Similarly, when a number is raised to the power 0, it will be 1.

Example: 20 = 1

The properties of exponents have been explained in the following points:

i. As already seen above, if we take any non-zero integer ‘n’ and raise it to the power -x, then n-x will be (1/nx ). Here ‘x’ is the positive integer, and n-x is the multiplicative inverse of nx

ii. For any non-zero integer ‘n’, nx/ny can be written as n(x-y)

Here, x and y are also positive integers and x>y.

Example:

43/42=4

iii. For any non zero integer ‘n’, nx x nx can be written as n( x+y)

Here, x and y are integers.

Example:

43x42=45

iv. (nx)y = nxy

Example

(42)2=44

v. nx × mx = (mn)x

Example:

(-4)2x(-4)-4 =(-4)2-4

(1/42)= 1/16

vi. nx / mx = (n/m)x

Example:

(-4)2/(-4)-4=(-4)2-(-4)=(-4)6

v. n0 =1

Example, 100=1

Let us see some factual numbers and how they can be represented in exponential form:

i. Our earth is 14960000000m from the sun.

ii. Speed of light is 300,000,000 m/sec.

iii. Earth is approximately 384, 467 000 m from the moon.

iv. The average diameter of RBC in our body is 0.000007 mm.

v. Sun’s radius on an average is 695000 km.

These were just some examples where we saw that the numbers could be very big and very small in decimals.** Exponents and powers** are used to represent such values easily.

Example

150,000,000,000 can be represented as 1.5 × 1011

Similarly, 0.000000008 can be written as 8/ 109 = 8 x 10-9

**Why are exponents and powers used?**

When we have very large or minimal values while solving any problem, there are chances of errors while writing the complete numbers. In this situation, they are represented in an exponential form that makes the simplification process easier.

**What are the five rules of exponents?**

The five rules of exponents are a multiplication of powers with the same base and with same exponents, division of powers with the same base, power of a power, negative exponents, and power with exponent zero.

**What’s the power rule for exponents?**

- When a number ‘n’ is raised to the power ‘x,’ and the same number is raised to the power’ y’, then multiplying these two numbers, the exponents are multiplied.
- If ‘n’ is raised to the power ‘x’ and the n to the power x is raised to the power y, then the value is calculated by raising n raised to the product of x and y.
- If ‘n’ is raised to the power ‘x’ and another number ‘m’ is raised to the power ‘y’, then the value is calculated by multiplying the bases, i.e., m x n, raised to the power of x x y.

**What is the 5th power of 3?**

The 5th power of 3 is represented in exponential form as 35, which is 243.

**How do you calculate exponential powers?**

We use the **properties of exponents **for simplifying the exponential powers.

Here we have explained the basic concept of **exponents and powers **in a nutshell. You can refer to the MSVGo app for further clarification of these concepts in a comprehensive way. There are visual illustrations and different examples to ensure an in-depth understanding of the topic. You will have complete clarity and will be in a position to solve even the most complex problems quickly. Since this is a concept used in most of the chapters in mathematics, you need to practice various types of problems to get a good grasp of it. MSVGo website offers a wide range of problems on every chapter, making it one of the best resources for you to refer to.

- Rational Numbers
- Linear Equations in One Variable
- Understanding Quadrilaterals
- Practical Geometry
- Data Handling
- Squares and Square Roots
- Cubes and Cube Roots
- Comparing Quantities
- Algebraic Expressions and Identities
- Visualizing Solid Shapes
- Mensuration
- Direct and Inverse Proportions
- Factorization
- Introduction to Graphs
- Playing With Numbers