Caret — Definition, Formula & Examples
The caret (^) is the symbol used to indicate exponentiation, meaning "raised to the power of." For example, 3^2 means 3 raised to the 2nd power, or 3 squared.
In mathematical notation—particularly in typed or digital contexts where superscript formatting is unavailable—the caret symbol (^) serves as the exponentiation operator, placed between a base and its exponent to denote repeated multiplication of the base.
Key Formula
a\text{^}b = a^b
Where:
- = The base — the number being multiplied by itself
- = The exponent — how many times the base is multiplied
How It Works
You use the caret when you cannot write a superscript, such as when typing on a calculator, in a spreadsheet, or in a programming language. Writing ^ is the same as writing , which means . The number before the caret is the base, and the number after is the exponent. Many graphing calculators and tools like Google Sheets, Excel, and Python use the caret (or a similar operator) for powers.
Worked Example
Problem: Evaluate 4^3 (typed with a caret).
Read the notation: The caret tells you to raise 4 to the 3rd power.
4\text{^}3 = 4^3
Expand: Write the base multiplied by itself the number of times indicated by the exponent.
Calculate: Multiply step by step: 4 × 4 = 16, then 16 × 4 = 64.
Answer: 4\text{^}3 = 64
Why It Matters
You will encounter the caret constantly when using graphing calculators, spreadsheets, and coding languages like Python. Recognizing that ^ means exponentiation lets you correctly enter and interpret formulas in tools like Excel (e.g., =2^10) or scientific calculators.
Common Mistakes
Mistake: Confusing the caret with multiplication, reading 3^4 as 3 × 4 = 12.
Correction: The caret means exponentiation, not multiplication. 3^4 = 3 × 3 × 3 × 3 = 81, not 12.