CHAPTER 11: EXPONENTS AND POWERS

What are Exponents and Powers?

Exponents are a shortcut for repeated multiplication! Instead of writing 2×2×2×2×2, we write 2⁵ (2 to the power 5).

Simple Example:

5 × 5 × 5 = 5³ (5 cubed)

2 × 2 × 2 × 2 = 2⁴ (2 to the power 4)

10 × 10 = 10² (10 squared)

The small number tells how many times to multiply!

Real-Life Examples

Chess Board:

A chess board has 8×8 = 64 squares

We can write: 8² = 64

That's why it's called "squaring"!

Computer Memory:

1 Kilobyte = 1024 bytes = 2¹⁰

1 Megabyte = 1024 KB = 2²⁰

Computers use powers of 2!

Area Calculation:

Area of square = side × side

If side = 5 cm, area = 5² = 25 cm²

The small ² means "squared"

Special Powers

Squares:

Any number to power 2

3² = 9, 4² = 16, 5² = 25

Called "square" because of area

Cubes:

Any number to power 3

2³ = 8, 3³ = 27, 4³ = 64

Called "cube" because of volume

Power of 10:

10¹ = 10, 10² = 100, 10³ = 1000

Used in scientific notation

What You Will Learn

In this chapter, we will learn:

  • What are exponents and powers
  • How to read and write powers
  • Laws of exponents
  • How to multiply powers
  • How to divide powers
  • Power of a power
  • Numbers with exponent zero
  • Standard form of numbers

Why is it Important?

Exponents and powers help us:

  • Write very large numbers easily
  • Understand computer memory sizes
  • Calculate areas and volumes
  • Work with scientific notation
  • Solve growth problems (population, bacteria)
  • Understand patterns in mathematics
  • Prepare for science and engineering
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For Class 7 Students (NCERT & JKBOSE)