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!
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"
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
In this chapter, we will learn:
Exponents and powers help us:
For Class 7 Students (NCERT & JKBOSE)