Key takeaways
- result = baseⁿ, meaning the base multiplied by itself n times.
- 5³ means 5 × 5 × 5 = 125, not 5 × 3 = 15.
- Any nonzero number to the power of 0 equals 1.
- Any number to the power of 1 stays unchanged.
In this guide
What is an exponent?
An exponent (also called a power) tells you how many times to multiply a number, called the base, by itself. In 5³, 5 is the base and 3 is the exponent, meaning 5 × 5 × 5.
Why does the exponent matter?
Exponents are how math describes fast growth or fast shrinkage: the volume of a cube, the spread of a virus, or the balance on a savings account earning compound interest all rely on repeated multiplication.
2¹⁰ isn't 20 — it's 1,024. Exponents grow far faster than multiplication, which is exactly why compound interest can turn small savings into a large amount over many years.
The formula
| Symbol | What it means | Example |
|---|---|---|
| result | The final answer after raising the base to the power | 125 |
| base | The number being multiplied by itself | 5 |
| n | The exponent, how many times the base is multiplied by itself | 3 |
How to calculate a power step by step
- 1Identify the base (the number being multiplied) and the exponent (how many times to multiply it).
- 2Write the base out that many times, connected by multiplication signs:
5 × 5 × 5. - 3Multiply them together step by step, from left to right:
5 × 5 = 25, then25 × 5 = 125. - 4The final product is your answer.
Enter your own base and exponent in the calculator below to see every multiplication step.
Try it yourself
Pre-filled with the example — change any value.
Common mistakes to avoid
- Forgetting that any number to the power of 0 equals 1. For example, 7⁰ = 1, not 0.
- Mixing up exponents with [square roots](/calculator/square-root). Squaring a number multiplies it by itself; the square root does the opposite, finding what number was squared.
- Losing track of negative bases. A negative base raised to an even power becomes positive, but stays negative for an odd power.
Tips and tricks
- Break a large exponent into smaller steps, like calculating 2⁶ as
2³ × 2³ = 8 × 8 = 64. - Check your answer by taking the appropriate root — the square root undoes a power of 2, the cube root undoes a power of 3.
- Exponents make scientific notation possible, and drive the growth in compound interest.
Where you'll use it in real life
- Geometry: calculating the volume of a cube (side³) or the area of a square (side²).
- Finance: modeling how an investment grows with compound interest, which uses exponents to represent repeated growth.
- Science: writing very large or very small numbers compactly, using powers of 10.
- Computing: memory and storage sizes are almost always powers of 2, like 1024 (2¹⁰) bytes in a kilobyte.
Quick summary
To raise a number to a power, multiply the base by itself as many times as the exponent says, working step by step from left to right. Any number to the power of 0 is 1, and to the power of 1 stays unchanged. Try the calculator above with your own base and exponent.
Worked example
A storage cube has sides that are each 5 cm long. Since volume equals side³, what is the volume of the cube in cubic centimeters?
- 01result = base^n
- 025^3 = 5 × 5 × 5
- 035^3 = 125
These numbers are pre-filled in the calculator above.
Frequently asked questions
What does it mean to "raise a number to a power"?
It means multiplying that number (the base) by itself as many times as the exponent says. Raising 4 to the power of 2 means 4 × 4 = 16.
What is a number raised to the power of 1?
It equals the number itself. Any base raised to the power of 1 stays unchanged, since it's only "multiplied by itself" once — meaning not multiplied at all.
What happens when the exponent is 0?
Any nonzero number raised to the power of 0 equals 1. This is a mathematical rule that keeps the pattern of exponents consistent.
What does a negative exponent mean?
A negative exponent means "1 divided by" the positive power. For example, 2⁻² means 1 ÷ 2², which equals 1/4 or 0.25.
