Exponent Calculator

Calculate powers, roots, and scientific notation. Learn exponent rules with step-by-step explanations and examples.

Formula:xⁿ = x × x × ... (n times)

Result

Answer

256

Expression2^8
Expanded2 × 2 × 2 × 2 × 2 × 2 × 2 × 2
Scientific2.5600 × 10^2

Calculation Type

Enter Values

^

28 = 256

Powers of 2

20 = 1
21 = 2
22 = 4
23 = 8
24 = 16
25 = 32
26 = 64
27 = 128
28 = 256
29 = 512
210 = 1,024
212 = 4,096
216 = 65,536
220 = 1,048,576
224 = 16,777,216
232 = 4,294,967,296

Powers of 10

10-6 = 1e-6
10-5 = 1e-5
10-4 = 1e-4
10-3 = 1e-3
10-2 = 1e-2
10-1 = 1e-1
100 = 1
101 = 10
102 = 100
103 = 1,000
104 = 10,000
105 = 100,000
106 = 1,000,000
109 = 1e+9
1012 = 1e+12
1015 = 1e+15

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)

1² = 1
2² = 4
3² = 9
4² = 16
5² = 25
6² = 36
7² = 49
8² = 64
9² = 81
10² = 100
11² = 121
12² = 144

Perfect Cubes (n³)

1³ = 1
2³ = 8
3³ = 27
4³ = 64
5³ = 125
6³ = 216
7³ = 343
8³ = 512
9³ = 729
10³ = 1000
11³ = 1331
12³ = 1728

Result

Answer

256

Expression2^8
Expanded2 × 2 × 2 × 2 × 2 × 2 × 2 × 2
Scientific2.5600 × 10^2

?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

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.
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.
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.
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.
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.
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: 2025-01-15