WorkedMathGlossary

Exponent Calculator

Enter a base and an exponent below to instantly calculate the result, including negative and fractional exponents.

^
2^10
1024

How Exponents Work

b^n means multiply b by itself n times. The rules extend naturally to zero, negative, and fractional exponents rather than needing separate definitions for each case.

Worked example

Calculate 3^4.

3 × 3 × 3 × 3 = 81

3^4 = 81

A second example

Calculate 5^3.

5 × 5 × 5 = 125

5^3 = 125

Keep going

  • Exponents and logarithms undo each other by definition; the log calculator runs that same relationship in the opposite direction. Log Calculator
  • Exponential growth is repeated exponentiation applied over time; the exponential growth calculator adds a growth rate and number of periods on top of a single exponent. Exponential Growth Calculator

Frequently Asked Questions

What does an exponent mean?

An exponent tells you how many times to multiply the base by itself. 2^4 means 2 × 2 × 2 × 2 = 16.

What does a negative exponent mean?

A negative exponent means take the reciprocal: b^(-n) = 1 / b^n. For example, 2^(-3) = 1/8.

What does an exponent of 0 give you?

Any nonzero number raised to the power of 0 equals 1. This isn't arbitrary — it falls directly out of the pattern of dividing successive powers by the base (2³=8, 2²=4, 2¹=2, 2⁰=1).

What does a fractional exponent mean?

A fractional exponent represents a root. b^(1/2) is the square root of b, and b^(1/3) is the cube root. b^(m/n) means take the nth root of b, then raise it to the mth power.

What's the difference between (−2)² and −2²?

(−2)² means multiply −2 by itself: (−2) × (−2) = 4. But −2² applies the exponent before the negative sign under standard order of operations, so it means −(2²) = −4. The parentheses matter.

How do you multiply two powers with the same base?

Add the exponents: b^m × b^n = b^(m+n). For example, 2³ × 2² = 2⁵ = 32, which you can check directly: 8 × 4 = 32.

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