Exponents
An exponent says how many times to multiply a base by itself.
About this topic
An exponent tells you how many times to multiply a base by itself, so 2⁵ = 2 × 2 × 2 × 2 × 2 = 32. It is a compact way to write repeated multiplication and to describe very large numbers, areas (squares) and volumes (cubes).
Exponents grow quickly, which is why doubling and compounding become surprisingly big. Any non-zero number to the power zero is 1, and a power of 1 leaves the number unchanged. Key laws: when multiplying the same base, add the exponents (a² × a³ = a⁵); when dividing, subtract them; and raising a power to a power multiplies exponents. A negative exponent means a reciprocal, so 2⁻³ = 1/8.
A classic illustration is folding paper: each fold doubles the thickness, so after 10 folds you have 2¹⁰ = 1,024 layers. A virus that doubles every day grows from 1 to over a million in 20 days. Computer memory sizes, compound interest and population growth are all described with exponents.
Be careful with negatives: (−3)² is 9 but −3² is −9, because the exponent only applies to what is directly attached to it. Another common mistake is thinking 2³ is 2 × 3 = 6. It is 2 × 2 × 2 = 8. And remember that 0⁰ is a special case that is often treated as undefined or defined by convention.
Key ideas
- a³ = a × a × a
- Anything to the power 0 is 1
- Squares and cubes link to area and volume
Quick check
Use cases: where Exponents helps
- Homework: review the key idea behind Exponents before you start a problem set.
- Exam revision: use the quick check to test whether you can recall Exponents without notes.
- Visual learning: play with the interactive lab to see how Exponents changes when you adjust its inputs.
- Teaching a friend: explain Exponents in your own words, then compare your version with the key ideas.
Number and algebra skills are used in science, engineering, budgeting and computing.
Frequently asked questions
What is Exponents?
An exponent says how many times to multiply a base by itself.
What will I learn in Exponents?
a³ = a × a × a. Anything to the power 0 is 1. Squares and cubes link to area and volume.
Is Exponents part of Mathematics?
Yes. It is one of 200 Mathematics topics on LearnViz HighSchoolEdu, with 3 key ideas, a live animation and a quick check.
Does the Exponents lab work on a phone or tablet?
Yes. The animation resizes to fit your screen and supports touch, so you can drag, tap and slide with your finger.
How should I study Exponents?
Read the summary and key ideas first, play with the interactive lab to see the idea in motion, then answer the quick check. If you get a question wrong, go back to the key idea it tests.
Do I need an account, and is my progress saved?
No account is needed. Marking a topic as learned is saved in your own browser, so it stays on that device and is not sent to a server.