CLASS 8 MATHS · EXPONENTS AND POWERS

Laws of exponents and standard form

aᵐ × aⁿ = aᵐ⁺ⁿ, aᵐ ÷ aⁿ = aᵐ⁻ⁿ, a⁻ⁿ = 1/aⁿ. Standard form: k × 10ⁿ with 1 ≤ k < 10.

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Worked examples

Example 1 · level 1

2⁹ × 2⁸ ÷ 2⁸ = 2ˣ. Find x.

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2⁹ × 2⁸ = 2¹⁷.
2¹⁷ ÷ 2⁸ = 2⁹.
x = 9.

Answer: 9

Example 2 · level 2

Find the value of (2/7)⁻¹. (answer as a fraction)

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(2/7)⁻¹ = (7/2)¹ = 7/2.
Answer: 7/2.

Answer: 7/2

Example 3 · level 3

Write 0.00407 in standard form.

4.07 × 10³
4.07 × 10⁻²
4.07 × 10⁻⁴
4.07 × 10⁻³

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k = 4.07.
The decimal point moves 3 places right, so n = −3.
0.00407 = 4.07 × 10⁻³.

Answer: 4.07 × 10⁻³