Chapter 2 · ICSE Class 8 Mathematics

Exponents (Powers)

Extend your knowledge of exponents to include negative powers, and master the full set of exponent laws.

⚡ Chapter 2

Repeated multiplication written as an exponent The expression 2 times 2 times 2 times 2 shown equal to 2 to the power 4, illustrating what an exponent means 2 × 2 × 2 × 2 4 times 2⁴
2.1

Negative Integral Exponents

A negative exponent means taking the reciprocal of the base raised to the positive version of that exponent: a⁻ⁿ = 1/aⁿ.

1

Evaluate 2⁻³.

1/2³ = 1/8

2

Evaluate 5⁻².

1/5² = 1/25

2.2

Applying the Laws of Exponents

The laws you know — multiplying adds exponents, dividing subtracts exponents, a power to a power multiplies exponents — all still work even when exponents are negative.

1

Simplify: 3⁵ × 3⁻²

3⁵⁻² = 3³ = 27

2

Simplify: (2⁻¹)³

2⁻³ = 1/8

Practice

Exercises

1. Evaluate 4⁻².

2. Evaluate 10⁻³.

3. Simplify: 5³ × 5⁻¹

4. Simplify: 2⁷ ÷ 2⁻²

5. Simplify: (3⁻²)²

Next chapter — Chapter 3: Squares and Square Roots √ →