Calculate powers, roots, and scientific notation. Learn exponent rules with step-by-step explanations and examples.
Answer
256
Common exponent calculations
28 = 256
Interactive formula breakdown
The number being multiplied
How many times to multiply the base
The final value
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
Test your understanding of exponents and their rules
Practice with 6 problems to test your understanding.
Answer
256
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.
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.
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.
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
Answer
256