Exponent Calculator
Calculate powers and exponentials with step-by-step breakdown
Exponent Calculator – Guide & Information
What is an Exponent?
An exponent shows how many times the base is multiplied by itself. For example, 2³ = 2 × 2 × 2 = 8.
Zero Exponent Rule
Any non-zero number raised to the power 0 is always 1. Example: 5⁰ = 1.
One Exponent Rule
Any number raised to the power 1 equals itself. Example: 7¹ = 7.
Negative Exponents
Negative exponents represent the reciprocal of the base raised to the positive exponent. Example: 2⁻³ = 1 / 2³ = 1/8.
Fractional Exponents
Fractional exponents represent roots. Example: 9^(1/2) = √9 = 3, 27^(1/3) = ∛27 = 3.
Real-World Use
Exponents are used in finance (compound interest), science (population growth, radioactive decay), computing, and engineering.
Frequently Asked Questions
Can the base be negative?
Yes, but fractional exponents of negative bases are undefined in real numbers.
Can the exponent be a decimal?
Yes, decimal exponents are fractional powers and can represent roots.
What happens if the exponent is very large?
The result may overflow or display in scientific notation.
What is 0⁰?
0⁰ is generally considered undefined, so avoid using it.
Is there a fast way to calculate repeated multiplication?
Yes, you can use this calculator to see step-by-step expansion for small integers.
Example Calculations
Example 1
- Base = 2
- Exponent = 3
- 2³ = 2 × 2 × 2 = 8
Example 2
- Base = 5
- Exponent = 0
- 5⁰ = 1 (Zero exponent rule)
Example 3
- Base = 2
- Exponent = -2
- 2⁻² = 1 / 2² = 1 / 4 = 0.25
Example 4
- Base = 9
- Exponent = 0.5
- 9^(1/2) = √9 = 3
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