Exponent Rules
A free Algebra I lesson from the “Exponents and Polynomials” unit, with a worked example and practice problems including step-by-step solutions.
Exponent rules keep repeated multiplication organized. The operation changes the exponent: multiply powers by adding exponents, divide by subtracting, and raise a power to a power by multiplying exponents. In Exponents and Polynomials, students need more than a memorized rule: they need to recognize the structure, select a method, carry out the algebra cleanly, and interpret the answer in a graph, table, equation, or real context. The expanded practice now mixes skill fluency, transfer questions, and cumulative review so the lesson builds durable Algebra I readiness.
What you'll learn
- Multiply and divide powers with the same base
- Raise powers to powers
- Use zero and negative exponents
Worked example
Problem. Simplify (x^3)^4.
- A power raised to a power means repeated groups.
- Multiply the exponents: 3 x 4 = 12.
- (x^3)^4 = x^12.
- Connect the result back to Exponent Rules so the method and meaning are both clear.
Answer: x^12
Lesson preview: this page shows 5 practice items. The interactive activity contains 28 practice items and 15 quiz items (typed response and multiple choice). Counts include repeated prompts and variants.
Practice problems
1. Simplify x^4 times x^2.
Show solution
- Same base multiplication means add exponents.
- 4 + 2 = 6.
Answer: x^6
2. Simplify y^7 divided by y^3.
Show solution
- Same base division means subtract exponents.
- 7 - 3 = 4.
Answer: y^4
3. Simplify (a^2)^3.
Show solution
- Power to a power means multiply exponents.
- 2 x 3 = 6.
Answer: a^6
4. Simplify m^5 times m^6.
Show solution
- Add exponents with the same base.
- 5 + 6 = 11.
Answer: m^11
5. Simplify b^9 divided by b^4.
Show solution
- Subtract exponents.
- 9 - 4 = 5.
Answer: b^5
Practice this interactively with instant feedback and an AI tutor.
Practice Exponent Rules Take the free placement check