A free printable exponent rules worksheet for Grade 8 math.
By Kris Reddy, Ontario teacher · Updated October 16, 2026 · 29 questions (30 marks) · PDF + answer key
This free exponent rules worksheet gives Grade 8 students focused practice with powers and the laws of exponents. It starts with evaluating powers, including the tricky difference between (−3)2 and −32, then works through the product law, the quotient law, the power of a power law and zero exponents one at a time.
Students then judge true-or-false statements, simplify expressions that use several laws at once, and solve three real-world problems about bacteria, computer memory and the volume of a cube. Every answer in the key shows the working and was checked by computer. To print it, use the Download button above.
| Part | Skill practised | Marks |
|---|---|---|
| A | Evaluate powers, including negative bases | 4 |
| B | Product law | 4 |
| C | Quotient law | 4 |
| D | Power of a power and zero exponents | 4 |
| E | True or false? Fix the false ones | 2 |
| F | Simplify, then evaluate (work boxes) | 4 |
| G | Three real-world problems | 6 |
| H | Spot the mistake | 2 |
The exponent rules worksheet supports the Ontario Grade 8 math curriculum in the Number and Algebra strands, where students work with powers and the order of operations. A key-ideas box at the top lists every law students need.
A power is repeated multiplication. In 25, the base is 2 and the exponent is 5, so 25 = 2 × 2 × 2 × 2 × 2 = 32. The exponent tells you how many times the base is used as a factor, not what to multiply the base by. That's why 53 is 125, not 15.
Watch the brackets with negative numbers. In (−3)2 the whole −3 is squared, giving 9. In −32 only the 3 is squared, and the negative sign is applied after, giving −9. Part A of the exponent rules worksheet tests exactly this.
Each law is a shortcut for counting factors. They only work when the bases are the same.
| Law | Rule | Example |
|---|---|---|
| Product law | am × an = am+n | 23 × 24 = 27 |
| Quotient law | am ÷ an = am−n | 79 ÷ 74 = 75 |
| Power of a power | (am)n = am×n | (23)4 = 212 |
| Zero exponent | a0 = 1 (a ≠ 0) | 120 = 1 |
You can check the product law by writing it out: 23 × 24 is (2 × 2 × 2) × (2 × 2 × 2 × 2), which is seven 2s, or 27. The same laws are the reason multiplying in scientific notation works, so try the scientific notation worksheet next. For more background, see exponentiation on Wikipedia.
Divide a power by itself: 65 ÷ 65 = 1, because anything divided by itself is 1. The quotient law gives 65−5 = 60. Both methods must give the same answer, so 60 = 1. Question 12 on the exponent rules worksheet leads students to this idea, and Part E checks the common wrong answer, 80 = 0.
These questions match the exponent rules worksheet PDF, which has answer lines, a true-or-false table and work boxes.
Open each part to check the exponent rules worksheet answers. The printable key is on the last two pages of the PDF.
These are the errors that come up most when marking this exponent rules worksheet. Parts E and H target them directly.
For more practice, try the algebra basics quiz, the integers quiz and the Pythagorean theorem worksheet.
Yes. The worksheet and its answer key are free to download and print as one PDF, with no account needed.
The product law (am × an = am+n), the quotient law (am ÷ an = am−n), the power of a power law ((am)n = am×n) and the zero exponent law (a0 = 1). They only work when the bases are the same.
Divide a power by itself. 53 ÷ 53 = 1, and the quotient law also gives 53−3 = 50. Both answers must match, so 50 = 1. This works for any base except 0.
The brackets show what is being squared. (−3)2 = (−3)(−3) = 9, but −32 means −(3 × 3) = −9.
It is written for Grade 8 math and also works as review for Grade 9 math.
Ready to start? Use the Download button above to print the free exponent rules worksheet double-sided, and keep the answer key pages for marking.