Try These Examples
Common exponent calculations
Calculation Type
Enter Values
28 = 256
Exponent Calculation
Interactive formula breakdown
The number being multiplied
How many times to multiply the base
The final value
Powers of 2
Powers of 10
Exponent Rules
xᵃ × xᵇ = xᵃ⁺ᵇ
Example: 2³ × 2⁴ = 2⁷ = 128
xᵃ ÷ xᵇ = xᵃ⁻ᵇ
Example: 2⁵ ÷ 2² = 2³ = 8
(xᵃ)ᵇ = xᵃᵇ
Example: (2³)² = 2⁶ = 64
x⁰ = 1
Example: 5⁰ = 1
x⁻ⁿ = 1/xⁿ
Example: 2⁻³ = 1/8 = 0.125
x^(1/n) = ⁿ√x
Example: 8^(1/3) = ³√8 = 2
Perfect Squares & Cubes
Perfect Squares (n²)
Perfect Cubes (n³)
Practice Exponent Problems
Test your understanding of exponents and their rules
Practice with 6 problems to test your understanding.
Result
Answer
256
?How Do You Calculate Exponents?
An exponent indicates how many times to multiply a base by itself. For example, 2^3 = 2 x 2 x 2 = 8. Key rules: a^m x a^n = a^(m+n), a^m / a^n = a^(m-n), (a^m)^n = a^(mn), a^0 = 1, a^(-n) = 1/a^n. Negative exponents create fractions; fractional exponents represent roots.
What is an Exponent?
An exponent (or power) indicates how many times a number (the base) is multiplied by itself. In the expression b^n, b is the base and n is the exponent. Exponents are fundamental to mathematics, appearing in scientific notation, compound interest, exponential growth and decay, and countless mathematical formulas.
Key Facts About Exponents
- a^n means multiply a by itself n times: 2^3 = 2 x 2 x 2 = 8
- Any number to the power of 0 equals 1: a^0 = 1
- Negative exponent: a^(-n) = 1/a^n (reciprocal)
- Product rule: a^m x a^n = a^(m+n)
- Quotient rule: a^m / a^n = a^(m-n)
- Power rule: (a^m)^n = a^(m*n)
- Fractional exponent: a^(1/n) = nth root of a
- Scientific notation uses powers of 10: 3.5 x 10^6 = 3,500,000
Quick Answer
An exponent indicates how many times to multiply a base by itself. For example, 2^3 = 2 x 2 x 2 = 8. Key rules: a^m x a^n = a^(m+n), a^m / a^n = a^(m-n), (a^m)^n = a^(mn), a^0 = 1, a^(-n) = 1/a^n. Negative exponents create fractions; fractional exponents represent roots.
Frequently Asked Questions
What is an exponent?
An exponent indicates how many times a number (the base) is multiplied by itself. For example, 2³ = 2 × 2 × 2 = 8. The small raised number is the exponent (or power), and the larger number is the base.
What does a negative exponent mean?
A negative exponent means to take the reciprocal of the base raised to the positive exponent. For example, 2⁻³ = 1/(2³) = 1/8 = 0.125. The rule is: x⁻ⁿ = 1/xⁿ.
What is any number to the power of 0?
Any non-zero number raised to the power of 0 equals 1. For example, 5⁰ = 1, 100⁰ = 1. This is because xⁿ/xⁿ = x⁰ = 1. Note: 0⁰ is undefined or sometimes defined as 1 depending on context.
How do I multiply exponents with the same base?
When multiplying powers with the same base, add the exponents: xᵃ × xᵇ = xᵃ⁺ᵇ. For example, 2³ × 2⁴ = 2⁷ = 128. When dividing, subtract exponents: xᵃ ÷ xᵇ = xᵃ⁻ᵇ.
What is a fractional exponent?
A fractional exponent like x^(1/n) means the nth root of x. For example, 8^(1/3) = ³√8 = 2. More generally, x^(m/n) = (ⁿ√x)ᵐ. So 8^(2/3) = (³√8)² = 2² = 4.
What is scientific notation?
Scientific notation expresses numbers as a coefficient (1-10) times a power of 10. For example, 3,000,000 = 3 × 10⁶ and 0.00045 = 4.5 × 10⁻⁴. It's useful for very large or small numbers.
Last updated: 2026-01-15
How this works
Formulas follow standard definitions from the NIST Digital Library of Mathematical Functions and classical textbook derivations. Calculations run entirely in your browser. Where a closed-form solution exists, it is used; where an iterative or numerical method is required, the implementation is named on the page.
Sources
- [1]NIST Digital Library of Mathematical FunctionsAcademicdlmf.nist.govAccessed Apr 21, 2026
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