ganak.appExponent Calculator
Calculate any exponent with free step-by-step solutions. Supports positive, negative, zero, and fractional exponents. See results in decimal, fraction, and scientific notation. Includes exponent rules, powers reference table, and common mistakes section.
Result Formats
The result displayed in multiple formats
Step-by-Step Solution
See how the answer is calculated — free, no paywall
aⁿ = a × a × ... × a (n times)
2^10
2^10
= 1,024
Powers of 2
Quick reference table for 2⁰ through 2¹²
How to Calculate Exponents
Understanding base, power, and the exponentiation formula
An exponent tells you how many times to multiply a number (the base) by itself. In the expression an, a is the base and n is the exponent (also called the power or index). The result is called a "power" — for example, 25 = 32 means "32 is the fifth power of 2."
Exponent Formula
an = a × a × ... × a (n times)
This calculator handles all exponent types: positive integers, negative exponents (reciprocals), zero exponent (always 1), fractional exponents (roots), and decimal exponents. Results are shown in multiple formats including decimal, fraction, and scientific notation.
Exponent Laws & Rules
The fundamental rules that govern how exponents work
Product Rule
am × an = am+n
When multiplying like bases, add the exponents
Quotient Rule
am ÷ an = am−n
When dividing like bases, subtract the exponents
Power Rule
(am)n = am×n
A power raised to a power multiplies the exponents
Negative Exponent
a−n = 1 / an
A negative exponent means take the reciprocal
Zero Exponent
a0 = 1 (for a ≠ 0)
Any non-zero number to the power of zero is 1
Fractional Exponent
a1/n = n√a
A fractional exponent represents a root
Common Mistakes with Exponents
Avoid these frequent errors when working with powers
−4² ≠ (−4)²
−4² = −16 (only 4 is squared), but (−4)² = 16 (the negative is included). Parentheses matter!
Adding instead of multiplying
2³ is not 2 × 3 = 6. It is 2 × 2 × 2 = 8. The exponent counts multiplications, not a scalar multiply.
Distributing exponents over addition
(a + b)² ≠ a² + b². You must FOIL: (a + b)² = a² + 2ab + b². Exponents do not distribute over sums.
Confusing negative and fractional exponents
a−2 = 1/a² (reciprocal), while a1/2 = √a (square root). These are very different operations.
Real-World Applications
Where exponents are used in everyday life and science
Compound Interest
The formula A = P(1 + r/n)nt uses exponents to model how money grows over time with compounding.
Population Growth
Bacteria double every generation: after n doublings, the count is 2n. Starting with 1, after 10 generations there are 1,024 bacteria.
Scientific Notation
Scientists use exponents to express very large or small numbers: the speed of light is 3 × 108 m/s, and an atom is ~10−10 meters.
Computer Science
Computers use powers of 2 everywhere: 210 = 1,024 bytes = 1 KB. Storage, memory, and data are measured in powers of 2.
Frequently Asked Questions
Common questions about exponents and powers