Exponent & Power Calculator

Raise any base number to a positive, negative, or fractional power instantly and review the working.

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A Helpful Guide to Solving Exponents

In mathematics, an exponent represents how many times a base number is multiplied by itself. For example, in the expression 2 raised to the power of 3, the number 2 is the base, and 3 is the exponent. This tells you to multiply 2 by itself three times (2 × 2 × 2 = 8). Exponents allow us to write and solve extremely large or small numbers efficiently.

Important Rules of Exponents

Exponents follow strict rules. A negative exponent indicates a reciprocal, meaning you turn the base into a fraction (for example, 2 raised to the power of -3 is one divided by 8). A fractional exponent represents a radical root (for example, raising a number to the power of one-half is the same as taking its square root).

Fractional powers are closely tied to roots, which you can solve using our finding mathematical roots tool. If you want to find what exponent was used to get a certain result, you can reverse the calculation using our logarithm calculations tool. For full formula support, check out our scientific calculator device tool.

Where Exponent Math is Used

Compound Savings: Interest in bank accounts accumulates exponentially, which you can model with our compound interest savings tool.
Computer Storage: Binary bytes grow by powers of two (2, 4, 8, 16, 32, 64...), defining memory sizes like megabytes and gigabytes.
Biological Growth: Viral spread and bacteria cell divisions double at set time intervals, creating exponential curves.
Scientific Notation: Astronomers use powers of ten to express distances across space, which you can calculate alongside a simple arithmetic tool.

The Special Zero Rule

One of the most unique properties in algebra is that any non-zero number raised to the power of zero is always equal to exactly one. Whether the base is 5, 100, or a decimal, raising it to the power of 0 results in 1.

This rule is consistent with how division works in exponents. Since dividing a number by itself equals one, dividing base^n by base^n (which equals base^(n-n) or base^0) must also equal one. This illustrates the beautiful logic built into algebra.

Example of a Fractional Power

Suppose you want to calculate 9 raised to the power of 1.5.

We can rewrite the decimal 1.5 as the fraction three-halves (3/2). According to the rules of fractional exponents, the denominator (2) means we take the square root of the base: square root of 9 is 3. The numerator (3) means we raise that result to the power of three: 3 raised to the power of 3 is 3 × 3 × 3 = 27. Thus, 9 raised to the power of 1.5 is exactly 27. This shows how fractional exponents combine roots and powers.