The Exponent Calculator computes the result of raising a base number to any power. It handles positive, negative, zero, and fractional exponents with precision.
Enter a base and an exponent to calculate the result. The tool supports large numbers and displays results in both standard and scientific notation when appropriate.
Your calculations will appear here
An exponent tells you how many times a number (the base) is multiplied by itself. For example, 2^5 means 2 multiplied by itself five times. Exponents are a compact way to represent repeated multiplication and appear throughout algebra, physics, and computer science.
Any non-zero number raised to the power 0 equals 1. By widely accepted convention, 0^0 is also defined as 1 in combinatorics and discrete mathematics. Any number raised to the power 1 equals itself.
A negative exponent indicates a reciprocal: a^(-n) = 1/a^n. A fractional exponent combines powers and roots: a^(m/n) = the nth root of a^m. These two ideas can be combined, so a^(-2/3) means 1 divided by the cube root of a squared.
The three fundamental rules are the product rule (a^m x a^n = a^(m+n)), the quotient rule (a^m / a^n = a^(m-n)), and the power rule ((a^m)^n = a^(m x n)). These rules simplify complex expressions and are essential for solving equations involving exponents.
Problem: Calculate 2^8
Solution: 2 multiplied by itself 8 times: 2 x 2 x 2 x 2 x 2 x 2 x 2 x 2 = 256.
Answer: 256
Problem: Convert 0.00047 to scientific notation
Solution: Move the decimal point 4 places to the right to get 4.7. Since the original number is less than 1, the exponent is negative.
Answer: 4.7 x 10^(-4)
Problem: Simplify 5^3 x 5^4
Solution: Using the product rule, 5^3 x 5^4 = 5^(3+4) = 5^7. Evaluating gives 78125.
Answer: 5^7 = 78125
Problem: Find the cube root of 64
Solution: The cube root of 64 is 4, because 4 x 4 x 4 = 64. Equivalently, 64^(1/3) = 4.
Answer: 4
Problem: Calculate 27^(-2/3)
Solution: 27^(-2/3) means 1 divided by the cube root of 27 squared. The cube root of 27 is 3, and 3 squared is 9, so the result is 1/9.
Answer: 0.111111 (or 1/9)
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