8 to the power of 2 equals 64. It is written $ 8^{2} $ and means multiplying 8 by itself 2 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 8 to the power of 2?
The expression 8 to the power of 2 is a shorthand for repeated multiplication. The base is 8 and the exponent 2 tells you how many times to use the base as a factor:
$$ 8^{2} = 8 \\times 8 = 64 $$Step-by-step calculation
Multiply one factor at a time:
- 81 = 8
- 82 = 64
So 8 to the power of 2 is 64.
8 to the power of 2 in different forms
| Form | Value |
|---|---|
| Standard form | 64 |
| Exponential form | 82 |
| Expanded form | 8 × 8 |
Powers of 8
Seeing the pattern makes exponents easier to remember:
| Power | Expanded | Value |
|---|---|---|
| 81 | 8 | 8 |
| 82 | 8 × 8 | 64 |
| 83 | 8 × 8 × 8 | 512 |
| 84 | 8 × 8 × 8 × 8 | 4,096 |
| 85 | 8 × 8 × 8 × 8 × 8 | 32,768 |
| 86 | 8 × 8 × 8 × 8 × 8 × 8 | 262,144 |
How to write and say 8 to the power of 2
In words it is “8 to the power of 2” (or “8 squared”). In math it is written with a small raised number called the exponent or index: $ 8^{2} $. The big number, 8, is the base. On most calculators you type it with the ^ or xⁿ key as 8^2, and in spreadsheets or code you write 8**2 or pow(8,2). All of these mean the same thing: multiply 8 by itself 2 times to get 64.
8 to the power of 2 vs 2 to the power of 8
Order matters with exponents. Swapping the base and exponent gives a completely different answer: while 8 to the power of 2 is 64, 2 to the power of 8 is 256. They are not the same, which is a common point of confusion — the base and the exponent play different roles.
What does squaring 8 mean?
Squaring a number gives the area of a square with that side length, so $ 8^2 = 64$ is the area of a 8-by-8 square. Squares appear throughout geometry, statistics (the squared errors behind regression) and distance formulas.
Frequently asked questions
What is 8 to the power of 2?
How do you calculate 8 to the power of 2?
What is 8 to the power of 2 in expanded form?
Is 8 to the power of 2 the same as 8 times 2?
What is 8 squared?
Related powers
Explore more worked exponents: 7 to the power of 3 9 to the power of 3 2 to the power of 10. 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.