🔼 Exponents & Roots

Last Updated: 06-Sep-2025

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What are Exponents?

An exponent means multiplying a number by itself many times.

👉 Example:

• $2^2$ = 2 x 2 = 4
• $3^3$ = 3 x 3 x 3 = 27
• $5^4$ = 5 x 5 x 5 x 5 = 625

Here,

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

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

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Special Exponents

• Any number to power 1 → Same number ($7^1$ = 7)
• Any number to power 0 → Always 1 ($5^0$ = 1)
• Negative power → Reciprocal
  • $2^{-2}$ = 1 / ($2^2$) = 1/4

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What are Roots?

A root is the reverse of exponent.

👉 Example:

• $\sqrt{9}$ = 3 (because $3^2$ = 9)
• $\sqrt{25}$ = 5 (because $5^2$ = 25)
• $\sqrt[3]{8}$ = 2 (cube root of 8, because $2^3$ = 8)

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

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Examples

• Square: Area of square = $side^2$
  • If side = 4 cm → area = 16 $cm^2$
• Cube: Volume of cube = $side^3$
  • If side = 3 cm → volume = 27 $cm^3$
• Square Root: Finding side length of a square if area is given
  • Area = 49 $cm^2$ → side = $\sqrt{49}$ = 7 cm

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Quick Practice

1. Find $2^5$.
2. Simplify $10^0$.
3. Find $\sqrt[3]{125}$.
4. What is the cube root of 125 ?
5. A square has area 81 $cm^2$. Find its side.

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