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Mathematics Class 7 - Exponents And-Powers Notes

Comprehensive study notes for Class 7 - Exponents And-Powers olympiad preparation

Exponents and Powers

Welcome to the chapter on Exponents and Powers for Class 7. In this chapter, you will learn what exponents are, how to use them, and how to solve problems using the laws of exponents. By the end of this chapter, you will be able to simplify expressions and solve sums confidently!

Introduction

Exponents are a way to show repeated multiplication of the same number. The exponent tells us how many times to multiply the base number by itself.

  • Example: 23 = 2 × 2 × 2 = 8
  • Here, 2 is the base and 3 is the exponent.

Reading Exponents

  • 52 is read as "five raised to the power two" or "five squared".
  • 34 is read as "three raised to the power four".

Laws of Exponents

  • Product Law: am × an = am+n
  • Quotient Law: am ÷ an = am-n
  • Power Law: (am)n = am×n
  • Zero Exponent: a0 = 1 (where a ≠ 0)
  • Negative Exponent: a-n = 1/an

Standard Form

Large numbers can be written in standard form using exponents.

  • Example: 1000 = 103
  • 1,000,000 = 106

Fun Activity: Exponent Hunt!

Write down numbers you see around you and try to express them using exponents. For example, 64 = 26 or 43.

Summary

  • Exponents show repeated multiplication.
  • Laws of exponents help us simplify expressions.
  • Standard form makes big numbers easy to write.

Practice Questions

  1. Write 3 × 3 × 3 × 3 using exponents.
  2. Simplify: 24 × 23
  3. Find the value of 50.
  4. Express 1/9 as a power of 3.
  5. Simplify: (42)3

Challenge Yourself

  • Write 1,000,000 as a power of 10.
  • Simplify: 75 ÷ 72

Did You Know?

  • Exponents are used in science to write very big or very small numbers!
  • The word "exponent" comes from Latin, meaning "to put forth".

Glossary

  • Exponent: The small number that shows how many times to multiply the base.
  • Base: The number that is multiplied.
  • Power: The result of multiplying the base by itself as many times as the exponent shows.
  • Standard Form: Writing numbers using exponents.

Answers to Practice Questions

  1. 34
  2. 27
  3. 1
  4. 3-2
  5. 46

Practice exponents and powers to make math easier and more fun!

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