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Exponents and Powers Class 7 Notes Maths Chapter 10

When the numbers given are very large like 54,32,00,00,000 then it is not easy to read them so we write them in the form of exponents.
Exponents make these numbers easy to read, write, understand and compare.

Exponents

To write the large numbers in short form, we use exponents.
Exponents and Powers Class 7 Notes Maths Chapter 10Here 8 is the base, 3 is the exponent and 83 is the exponential form of 512.
This can be read as “8 raised to the power of 3”.

The Expanded form of Natural Numbers

When we write the expanded form of a natural number then it can be written in exponential form.
Example: 247983 = 2 × 100000 + 4 × 10000 + 7 × 1000 + 9 × 100 + 8 × 10 + 3 × 1
= 2 × 105 + 4 × 104 + 7 × 103 + 9 × 102 + 8 × 101 + 3 × 1

Some Important Points to Remember

  • (-1)odd number = (-1)
  • (-1)even number = (1)
  • a3b2 ≠ a2b3
  • a2b3 = b3a2

Laws of Exponents

1. How to multiply powers with the same base?

If we have to multiply the powers which have the same base then we have to add the exponents.
am × an = am + n
Example: 83 × 84 = 83 + 4 = 87

2. How to divide powers with the same base?

If we have to divide the powers which have the same base then we have to subtract the exponents.
Exponents and Powers Class 7 Notes Maths Chapter 10
Example: Exponents and Powers Class 7 Notes Maths Chapter 10

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3. How to take the power of a power?

If we have to take the power of a power then we have to multiply the exponents.
(am)n = amn
Example: (83)4 = 83 × 4 = 812

4. How to multiply the powers with the same exponents?

If we have to multiply the powers where the base is different but exponents are same then we will multiply the base.
ambm = (ab)m
Example: 8343 = (8× 4)= 323

5. How to divide the powers with the same exponents?

If we have to divide the powers where the base is different but exponents are same then we will divide the base.
Exponents and Powers Class 7 Notes Maths Chapter 10
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Exponents and Powers Class 7 Notes Maths Chapter 10

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6. Numbers with Exponent Zero

Any number with zero exponents is equal to one irrespective of the base.
a°= 1
Example: 8° = 1

7. Numbers with Exponent One

Any number with one as the exponent is equal to the number itself.
a1 = a

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Example: 81 = 8


8. Power with a Negative Exponent

Negative exponents can be converted into positive exponents.
Exponents and Powers Class 7 Notes Maths Chapter 10
Example:Exponents and Powers Class 7 Notes Maths Chapter 10

Miscellaneous Examples

Example 1:
Exponents and Powers Class 7 Notes Maths Chapter 10 

Example 2:
Exponents and Powers Class 7 Notes Maths Chapter 10

Expressing Large Numbers in the Standard Form

If we have to write very large numbers then to make them easy to read and understand we can write them in the standard form using decimals and exponents from 1.0 to 10.0.
85 = 8.5 × 10 = 8.5 × 101
850 = 8.5 × 100 = 8.5 × 102
8500 = 8.5 × 1000 = 8.5 × 103
8500 = 8.5 × 10000 = 8.5 × 10and so on.

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FAQs on Exponents and Powers Class 7 Notes Maths Chapter 10

1. What are exponents and how are they used in mathematics?
Ans. Exponents represent how many times a number is multiplied by itself. They are used to express large numbers in a more concise form and are an important concept in mathematics for simplifying calculations.
2. How do you write the expanded form of natural numbers using exponents?
Ans. The expanded form of a natural number using exponents involves breaking down the number into its place value components and writing it as a sum of each place value multiplied by the corresponding power of 10.
3. What are the laws of exponents and how do they work?
Ans. The laws of exponents include rules for multiplying, dividing, and raising exponents to a power. These laws help simplify calculations involving exponents and powers by providing guidelines for manipulating them.
4. How can understanding exponents and powers benefit students in their mathematical studies?
Ans. Understanding exponents and powers can help students simplify complex mathematical expressions, solve equations more efficiently, and grasp concepts in higher-level math courses such as algebra and calculus.
5. Can you provide some real-life examples of how exponents are used outside of the classroom?
Ans. Exponents are commonly used in science to represent quantities like populations, radioactive decay, and growth rates. They are also used in finance to calculate compound interest and in computer science for data storage capacities.
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