A one-page reference for the Year 8 index laws: multiplying and dividing powers with the same base, raising a power to a power, the zero index and powers of a product. Each law has a numeric and an algebraic example, and the worked examples show how to handle coefficients alongside the indices.
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Curriculum: Australian Curriculum. We show specific outcome codes only where they have been verified against the official curriculum document.
Completed: Index Laws Cheat Sheet
Year 8 students (typically ages 13–14) working on indices & scientific notation. It is pitched at level 2 · standard.
This is a study guide, so there is no separate answer sheet; the 'Check yourself' questions include answers.
About 15 minutes. Short, regular sessions work best: two or three a week beats one long one.
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Try Year 8 Index Laws Worksheet — Level 2.
Year 8 · Mathematics · Indices & Scientific Notation
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In 25, the base is 2 and the index (also called the power or exponent) is 5. It means 2 × 2 × 2 × 2 × 2 = 32. The index laws are shortcuts that let you simplify expressions without writing out all the multiplications. Every law below only works when the terms have the same base.
| Law | Rule | Number example | Algebra example |
|---|---|---|---|
| Multiplying | am × an = am + n | 34 × 32 = 36 | x5 × x3 = x8 |
| Dividing | am ÷ an = am − n | 57 ÷ 53 = 54 | y9 ÷ y2 = y7 |
| Power of a power | (am)n = am × n | (23)4 = 212 | (k2)5 = k10 |
| Zero index | a0 = 1 (a ≠ 0) | 90 = 1 | (7x)0 = 1 |
| Power of a product | (ab)m = ambm | (2 × 5)3 = 23 × 53 = 1000 | (2x)3 = 8x3 |
Simplify 23 × 24
Simplify 6x5 ÷ 2x2
Simplify (3a2)3
Why is 50 equal to 1?
Terms with more than one letter. Handle the coefficients first, then each base separately. 4m2n × 3mn3: coefficients 4 × 3 = 12; m2 × m = m3 (remember m means m1); n × n3 = n4. Result: 12m3n4.
Answers: 1. 77 2. x6 3. 56 4. 1 5. 20a5 6. 8y12
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