Chapter 7 · ICSE Class 9 Mathematics (Selina Concise)

Indices [Exponents]

Apply the laws of indices, including fractional and negative exponents, to simplify expressions.

🔋 Chapter 7

The laws of indices: multiplying and dividing powers with the same base Two exponent laws shown: a to the power m times a to the power n equals a to the power m plus n, and a to the power m divided by a to the power n equals a to the power m minus n aᵐ × aⁿ = aᵐ⁺ⁿ aᵐ ÷ aⁿ = aᵐ⁻ⁿ Example: 2³ × 2² = 2⁵ = 32
7.1

Laws of Indices

aᵐ×aⁿ=aᵐ⁺ⁿ, aᵐ÷aⁿ=aᵐ⁻ⁿ, (aᵐ)ⁿ=aᵐⁿ, and a⁰=1 (for a≠0). These rules let us simplify complex exponential expressions.

1

Simplify: 2³×2⁴

2⁷=128

2

Simplify: (3²)³

3⁶=729

3

Simplify: 3⁵÷3²

3³=27

7.2

Fractional and Negative Indices

A fractional index represents a root: a^(1/n)=ⁿ√a. A negative index means taking the reciprocal: a⁻ⁿ=1/aⁿ.

1

Evaluate: 27^(1/3)

∛27=3

2

Evaluate: 2⁻⁴

1/2⁴=1/16

3

Evaluate: 32^(1/5)

⁵√32=2

Practice

Exercises

1. Simplify: 5²×5³

2. Simplify: (2³)²

3. Evaluate: 64^(1/3)

4. Evaluate: 3⁻²

5. Simplify: (16)^(3/4)

6. Simplify: 7²×7³

7. Simplify: (4³)²

8. Evaluate: 216^(1/3)

9. Evaluate: 4⁻³

10. Evaluate: 81^(3/4)

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