Exponent Calculator
Powers and exponents
How Exponents Work
An exponent tells you how many times to multiply a number (the base) by itself. For example, 2^10 means multiply 2 by itself 10 times, which equals 1,024. Exponents are also called powers. This calculator supports any base and exponent, including negative and fractional exponents.
Special Exponent Rules
Any number raised to the power of 0 equals 1. Any number raised to the power of 1 equals itself. Negative exponents create fractions: 2^(-3) = 1/8. Fractional exponents create roots: 8^(1/3) = 2 (cube root of 8).
Exponent Calculator: practical guide
The Exponent Calculator is built for people who want a fast answer without losing context. It keeps the calculation simple, shows the result clearly, and helps you understand what the number means before you use it in a real decision.
This calculator is designed to make a specific everyday calculation faster and clearer. It gives a structured result so you can compare options, check assumptions, or plan the next step with less manual work.
What is the best way to use the Exponent Calculator?
Enter the values carefully, review the units, and use the result as a reliable reference point. The Exponent Calculator is most useful when you compare scenarios or repeat the calculation with consistent inputs.
Is the Exponent Calculator accurate?
The calculator follows standard calculation logic, but accuracy depends on the values you enter and the assumptions behind the formula. For important math decisions, use it as guidance and verify the result with a trusted source.
What are exponents?
An exponent (also called a power or index) indicates how many times a number (the base) is multiplied by itself. The expression 2⁵ means 2 × 2 × 2 × 2 × 2 = 32. The base is 2 and the exponent is 5. Exponents appear in scientific notation, compound interest calculations, computer storage (powers of 2), physics equations, and algebra.
Notation: b^n means b raised to the power n. b is the base, n is the exponent.
Exponent rules — the complete reference
Product rule: b^m × b^n = b^(m+n)
Example: 3^4 × 3^2 = 3^6 = 729
Quotient rule: b^m ÷ b^n = b^(m–n)
Example: 5^7 ÷ 5^3 = 5^4 = 625
Power rule: (b^m)^n = b^(m×n)
Example: (2^3)^4 = 2^12 = 4,096
Zero exponent: b^0 = 1 (for any non-zero b)
Example: 7^0 = 1, 1000^0 = 1, (–5)^0 = 1
Negative exponent: b^(–n) = 1 ÷ b^n
Example: 2^(–3) = 1/2^3 = 1/8 = 0.125
Fractional exponent: b^(1/n) = nth root of b
Example: 27^(1/3) = ∛27 = 3. 16^(1/4) = ⁴√16 = 2
Fractional exponent (m/n): b^(m/n) = (nth root of b)^m
Example: 8^(2/3) = (∛8)² = 2² = 4
Common powers reference table
- 2^10 = 1,024 ≈ 1 thousand | 2^20 = 1,048,576 ≈ 1 million | 2^30 ≈ 1 billion (computer storage: KB, MB, GB)
- 10^3 = 1,000 (kilo) | 10^6 = 1,000,000 (mega) | 10^9 (giga) | 10^12 (tera)
- 3^2 = 9 | 4^2 = 16 | 5^2 = 25 | 6^2 = 36 | 10^2 = 100 | 12^2 = 144
- 2^3 = 8 | 3^3 = 27 | 4^3 = 64 | 5^3 = 125 | 10^3 = 1,000
Scientific notation — exponents in science
Scientific notation expresses very large or very small numbers as a number between 1 and 10 multiplied by a power of 10.
- Distance to the Sun: 149,597,870 km = 1.496 × 10^8 km
- Size of a hydrogen atom: 0.000000000106 m = 1.06 × 10^(–10) m
- Speed of light: 299,792,458 m/s = 2.998 × 10^8 m/s
Multiplying numbers in scientific notation: multiply the coefficients and add the exponents. (3 × 10^4) × (2 × 10^6) = 6 × 10^10
Exponents in compound interest — the financial connection
The compound interest formula A = P(1 + r/n)^(nt) uses an exponent (nt) to model how money grows over time. The exponent represents the number of compounding periods, and exponential growth is why compound interest is so powerful over long periods. At 10% annual interest, $100,000 grows to $110,000 after 1 year but $672,750 after 20 years — the exponent of 20 multiplies the growth dramatically.
Frequently asked questions about exponents
What is any number to the power of 1? Any base to the power of 1 equals itself. 7^1 = 7. 1,000^1 = 1,000.
What is 0 to the power of 0? 0^0 is mathematically indeterminate — it has no single well-defined value. In most computing and mathematical contexts, it is treated as 1 by convention, but this is context-dependent.
What is a negative base raised to an exponent? A negative base raised to an even exponent gives a positive result. A negative base raised to an odd exponent gives a negative result. (–3)^2 = 9. (–3)^3 = –27.