3 to the power of 6 equals 729. It is written $ 3^{6} $ and means multiplying 3 by itself 6 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 3 to the power of 6?
The expression 3 to the power of 6 is a shorthand for repeated multiplication. The base is 3 and the exponent 6 tells you how many times to use the base as a factor:
$$ 3^{6} = 3 \\times 3 \\times 3 \\times 3 \\times 3 \\times 3 = 729 $$Step-by-step calculation
Multiply one factor at a time:
- 31 = 3
- 32 = 9
- 33 = 27
- 34 = 81
- 35 = 243
- 36 = 729
So 3 to the power of 6 is 729.
3 to the power of 6 in different forms
| Form | Value |
|---|---|
| Standard form | 729 |
| Exponential form | 36 |
| Expanded form | 3 × 3 × 3 × 3 × 3 × 3 |
Powers of 3
Seeing the pattern makes exponents easier to remember:
| Power | Expanded | Value |
|---|---|---|
| 31 | 3 | 3 |
| 32 | 3 × 3 | 9 |
| 33 | 3 × 3 × 3 | 27 |
| 34 | 3 × 3 × 3 × 3 | 81 |
| 35 | 3 × 3 × 3 × 3 × 3 | 243 |
| 36 | 3 × 3 × 3 × 3 × 3 × 3 | 729 |
How to write and say 3 to the power of 6
In words it is “3 to the power of 6” (or the 6th power of 3). In math it is written with a small raised number called the exponent or index: $ 3^{6} $. The big number, 3, is the base. On most calculators you type it with the ^ or xⁿ key as 3^6, and in spreadsheets or code you write 3**6 or pow(3,6). All of these mean the same thing: multiply 3 by itself 6 times to get 729.
3 to the power of 6 vs 6 to the power of 3
Order matters with exponents. Swapping the base and exponent gives a completely different answer: while 3 to the power of 6 is 729, 6 to the power of 3 is 216. They are not the same, which is a common point of confusion — the base and the exponent play different roles.
Where exponents show up
Repeated multiplication like $ 3^{6} = 729$ models exponential growth — compound interest, population growth and the loss surfaces of machine learning all rely on it. Exponents grow fast, which is exactly why they are so useful for describing big changes with small numbers.
Frequently asked questions
What is 3 to the power of 6?
How do you calculate 3 to the power of 6?
What is 3 to the power of 6 in expanded form?
Is 3 to the power of 6 the same as 3 times 6?
Why do exponents grow so fast?
Related powers
Explore more worked exponents: 6 to the power of 4 4 to the power of 4 5 to the power of 2. 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.