9 to the power of 3 equals 729. It is written $ 9^{3} $ and means multiplying 9 by itself 3 times. Below is the step-by-step calculation, the different ways to write it, and a quick calculator to try any other base and exponent.
What is 9 to the power of 3?
The expression 9 to the power of 3 is a shorthand for repeated multiplication. The base is 9 and the exponent 3 tells you how many times to use the base as a factor:
$$ 9^{3} = 9 \\times 9 \\times 9 = 729 $$Step-by-step calculation
Multiply one factor at a time:
- 91 = 9
- 92 = 81
- 93 = 729
So 9 to the power of 3 is 729.
9 to the power of 3 in different forms
| Form | Value |
|---|---|
| Standard form | 729 |
| Exponential form | 93 |
| Expanded form | 9 × 9 × 9 |
Powers of 9
Seeing the pattern makes exponents easier to remember:
| Power | Expanded | Value |
|---|---|---|
| 91 | 9 | 9 |
| 92 | 9 × 9 | 81 |
| 93 | 9 × 9 × 9 | 729 |
| 94 | 9 × 9 × 9 × 9 | 6,561 |
| 95 | 9 × 9 × 9 × 9 × 9 | 59,049 |
| 96 | 9 × 9 × 9 × 9 × 9 × 9 | 531,441 |
How to write and say 9 to the power of 3
In words it is “9 to the power of 3” (or “9 cubed”). In math it is written with a small raised number called the exponent or index: $ 9^{3} $. The big number, 9, is the base. On most calculators you type it with the ^ or xⁿ key as 9^3, and in spreadsheets or code you write 9**3 or pow(9,3). All of these mean the same thing: multiply 9 by itself 3 times to get 729.
9 to the power of 3 vs 3 to the power of 9
Order matters with exponents. Swapping the base and exponent gives a completely different answer: while 9 to the power of 3 is 729, 3 to the power of 9 is 19,683. They are not the same, which is a common point of confusion — the base and the exponent play different roles.
What does cubing 9 mean?
Cubing a number gives the volume of a cube with that side length, so $ 9^3 = 729$ is the volume of a 9-by-9-by-9 cube. Cubes show up in geometry, scaling laws and volume calculations.
Frequently asked questions
What is 9 to the power of 3?
How do you calculate 9 to the power of 3?
What is 9 to the power of 3 in expanded form?
Is 9 to the power of 3 the same as 9 times 3?
What is 9 cubed?
Related powers
Explore more worked exponents: 2 to the power of 7 9 to the power of 2 7 to the power of 3. Exponents are undone by the logarithm (the inverse operation), and you can read the formal exponentiation reference on Wikipedia. Or try any values in the calculator above.