🔼 Exponents & Roots

Last Updated: 06-Sep-2025

What are Exponents?

An exponent means multiplying a number by itself many times.

👉 Example:

  • 2² = 2 × 2 = 4
  • 3³ = 3 × 3 × 3 = 27
  • 5⁴ = 5 × 5 × 5 × 5 = 625

Here,

  • 2, 3, 5 = base
  • ², ³, ⁴ = exponent (power)

Hinglish Tip 🗣 : Exponent = Number ko bar-bar multiply karna.

Special Exponents

  • Any number to power 1 → Same number (7¹ = 7)
  • Any number to power 0 → Always 1 (5⁰ = 1)
  • Negative power → Reciprocal
    • 2⁻² = 1 / (2²) = 1/4

What are Roots?

A root is the reverse of exponent.

👉 Example:

  • √9 = 3 (because 3² = 9)
  • √25 = 5 (because 5² = 25)
  • ∛8 = 2 (cube root of 8, because 2³ = 8)

Hinglish Tip 🗣 : Root = "Kaunsa number power me lene pe diya gaya number banta hai?"

Examples

  • Square: Area of square = side²
    • If side = 4 cm → area = 16 cm²
  • Cube: Volume of cube = side³
    • If side = 3 cm → volume = 27 cm³
  • Square Root: Finding side length of a square if area is given
    • Area = 49 cm² → side = √49 = 7 cm

⚡ Quick Practice

  1. Find 2⁵.
  2. Simplify 10⁰.
  3. Find √64.
  4. What is the cube root of 125?
  5. A square has area 81 cm². Find its side.
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