2 to the power of 10 equals 1,024. It is written $ 2^{10} $ and means multiplying 2 by itself 10 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 2 to the power of 10?
The expression 2 to the power of 10 is a shorthand for repeated multiplication. The base is 2 and the exponent 10 tells you how many times to use the base as a factor:
$$ 2^{10} = 2 \\times 2 \\times 2 \\times 2 \\times 2 \\times 2 \\times 2 \\times 2 \\times 2 \\times 2 = 1,024 $$Step-by-step calculation
Multiply one factor at a time:
- 21 = 2
- 22 = 4
- 23 = 8
- 24 = 16
- 25 = 32
- 26 = 64
- 27 = 128
- 28 = 256
- 29 = 512
- 210 = 1,024
So 2 to the power of 10 is 1,024.
2 to the power of 10 in different forms
| Form | Value |
|---|---|
| Standard form | 1,024 |
| Exponential form | 210 |
| Expanded form | 2 × 2 × 2 × 2 × 2 × 2 × 2 × 2 × 2 × 2 |
Powers of 2
Seeing the pattern makes exponents easier to remember:
| Power | Expanded | Value |
|---|---|---|
| 21 | 2 | 2 |
| 22 | 2 × 2 | 4 |
| 23 | 2 × 2 × 2 | 8 |
| 24 | 2 × 2 × 2 × 2 | 16 |
| 25 | 2 × 2 × 2 × 2 × 2 | 32 |
| 26 | 2 × 2 × 2 × 2 × 2 × 2 | 64 |
How to write and say 2 to the power of 10
In words it is “2 to the power of 10” (or the 10th power of 2). In math it is written with a small raised number called the exponent or index: $ 2^{10} $. The big number, 2, is the base. On most calculators you type it with the ^ or xⁿ key as 2^10, and in spreadsheets or code you write 2**10 or pow(2,10). All of these mean the same thing: multiply 2 by itself 10 times to get 1,024.
2 to the power of 10 vs 10 to the power of 2
Order matters with exponents. Swapping the base and exponent gives a completely different answer: while 2 to the power of 10 is 1,024, 10 to the power of 2 is 100. They are not the same, which is a common point of confusion — the base and the exponent play different roles.
Why powers of 2 matter
Powers of two are the backbone of computing. Because each bit doubles the count of values you can represent, $2^{10}=1,024$ shows up directly in memory sizes, addressing and binary numbers. For instance $2^{10}=1024$ is one kilobyte, and every extra bit doubles the range. That doubling is also why they appear in algorithms, hashing and the binomial distribution.
Frequently asked questions
What is 2 to the power of 10?
How do you calculate 2 to the power of 10?
What is 2 to the power of 10 in expanded form?
Is 2 to the power of 10 the same as 2 times 10?
Why do exponents grow so fast?
Related powers
Explore more worked exponents: 8 to the power of 2 7 to the power of 3 2 to the power of 8. 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.