Power Calculator

Calculate x raised to the power n (xn) with detailed step-by-step expansion.

Enter Base & Exponent

210 = 1024

Result

xn
1024
Base (x) 2
Exponent (n) 10
Result 1024
Scientific Notation 1.024e+3
Reciprocal (x-n) 0.000977
log10(result) 3.010300

Step-by-Step Solution

2^10 = 1024

Understanding Exponentiation

Exponentiation is one of the fundamental arithmetic operations. It involves raising a base number x to a power n, written as xn. The exponent tells you how many times to multiply the base by itself. For example, 23 = 2 * 2 * 2 = 8. This operation appears throughout mathematics, science, finance, and computer science.

Rules of Exponents

Product Rule

When multiplying same bases, add the exponents.

x^a * x^b = x^(a+b)

Quotient Rule

When dividing same bases, subtract the exponents.

x^a / x^b = x^(a-b)

Power of a Power

When raising a power to another power, multiply the exponents.

(x^a)^b = x^(a*b)

Zero Exponent

Any nonzero number raised to the power of 0 equals 1.

x^0 = 1 (x != 0)

Negative Exponent

A negative exponent means taking the reciprocal of the positive power.

x^(-n) = 1 / x^n

Fractional Exponent

A fractional exponent represents a root: x^(1/n) is the nth root of x.

x^(a/b) = (x^a)^(1/b)

Special Cases

  • x1 = x -- Any number to the power 1 is itself.
  • 1n = 1 -- 1 raised to any power is 1.
  • 0n = 0 (for n > 0) -- Zero raised to any positive power is 0.
  • 00 is conventionally defined as 1 in most contexts (combinatorics, algebra).
  • Negative base, even exponent: Result is positive. (-2)4 = 16.
  • Negative base, odd exponent: Result is negative. (-2)3 = -8.

Applications of Exponentiation

Exponentiation is used in compound interest calculations (A = P(1+r)n), exponential growth and decay models, binary representations in computing (powers of 2), physics formulas, and probability theory. Understanding powers is essential for algebra, calculus, and higher mathematics.