Class 7 Mathematics

Chapter 13: Exponents and Powers

                                       

STAGE 0: Foundation

Sometimes numbers are repeated again and again in multiplication. To make writing easy, we use exponents (powers).

Example:

2 × 2 × 2 × 2 = 2⁴

STAGE 1: What is an Exponent?

In the expression 2⁴:

• 2 is the base
• 4 is the exponent (power)

It means 2 is multiplied by itself 4 times.

STAGE 2: Writing Numbers in Exponential Form

Examples:

• 5 × 5 × 5 = 5³
• 10 × 10 = 10²
• 3 × 3 × 3 × 3 = 3⁴

STAGE 3: Laws of Exponents

Law 1: a^m × aⁿ = a^m+n

Example: 2³ × 2² = 2⁵

Law 2: a^m ÷ aⁿ = a^m−n (a ≠ 0)

Example: 5⁴ ÷ 5² = 5²

STAGE 4: Power of a Power

(a^m)ⁿ = a^m×n

Example:

(2³)² = 2⁶

STAGE 5: Power of 1 and Power of 0

• a¹ = a
• a⁰ = 1 (a ≠ 0)

Examples:

• 7¹ = 7
• 9⁰ = 1

STAGE 6: Large Numbers Using Powers of 10

10³ = 1000
10⁶ = 1,000,000

Powers of 10 help us write very large numbers easily.

STAGE 7: Practice Questions

1. Write 4 × 4 × 4 in exponential form.
2. Find the value of 2⁵.
3. Simplify: 3² × 3³.
4. Find the value of 7⁰.
5. Write 1,000,000 using powers of 10.

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Shaktimatha CBSE Learning
Class 7 Mathematics – Chapter 13: Exponents and Powers

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