Power Function Calculator: Calculate x to the n

Use this power function calculator to evaluate a number raised to an exponent, written as xⁿ. Enter the base and exponent to get the result; for example, it calculates 2⁵ as 32 and can also handle fractional or negative exponents within the real-number rules described below.

Formula

The power function is f(x) = xⁿ. In this calculator, base is x, the number being raised to a power, and exp is n, the exponent. The output is base multiplied by itself exp times when exp is a positive integer.

For example, x⁴ means x × x × x × x. Exponents are dimensionless counts in the usual arithmetic sense, so the calculator’s inputs and output have no assigned physical unit. If the base represents a measured quantity, its unit is raised to the exponent as well: for instance, a length in metres squared becomes an area in square metres.

Worked Example

With the default inputs, base = 2 and exp = 5:

1. Write the expression: 2⁵.
2. Multiply five copies of 2: 2 × 2 × 2 × 2 × 2.
3. Evaluate: 4 × 2 × 2 × 2 = 8 × 2 × 2 = 16 × 2 = 32.

The calculator returns 32, displayed to six decimal places as 32.000000.

What a Power Function Means

A power function describes how a fixed base changes when raised to a variable exponent, or how a fixed exponent transforms different bases. The notation xⁿ is also called exponentiation. The base and exponent play different roles: in 3², 3 is the base and 2 is the exponent; the answer is 9.

For a positive whole-number exponent, exponentiation is repeated multiplication. Other exponents follow consistent mathematical rules:

• Exponent zero: x⁰ = 1 for every nonzero x.
• Negative exponent: x⁻ⁿ = 1/xⁿ, provided x is not zero. For example, 2⁻³ = 1/8 = 0.125.
• Fractional exponent: x^(1/n) represents an nth root when that root is real. For example, 9^(1/2) = √9 = 3.
• Other rational exponents: x^(m/n) can be understood as an nth root followed by raising to m, subject to real-number restrictions.

How to Use the Calculator

• Enter the number to be raised in the Base field.
• Enter the power in the Exponent field. Use 2 for a square, 3 for a cube, or a negative or fractional value when appropriate.
• Read the result as the base raised to the exponent. The result is rounded to six decimal places for display; this does not mean the underlying value is necessarily exact to that many decimal places.

For a scientific-notation value such as 4.2 × 10⁶, first evaluate the power of ten or use the calculator’s base input only if you have rewritten the entire expression correctly. For example, (4.2 × 10⁶)² is 4.2² × 10¹² = 17.64 × 10¹², not 4.2 × 10¹².

Examples and Reading the Result

Changing the exponent can produce very different results even when the base stays fixed. With base 3, exponent 2 gives 9, exponent 0 gives 1, and exponent −2 gives 1/9, or about 0.111111. With base 10, exponent 3 gives 1,000, while exponent 0.5 gives √10, approximately 3.162278.

A negative base needs particular care. A negative base raised to an integer exponent is real: (−2)³ = −8, while (−2)⁴ = 16. Parentheses matter. The expression −2⁴ is conventionally interpreted as −(2⁴), which equals −16, whereas (−2)⁴ equals 16.

Some fractional powers of negative bases have real values and others do not. For example, (−8)^(1/3) has the real value −2, because the cube root of −8 is −2. But (−8)^(1/2) has no real-number result; its square root is complex. Calculator software can differ in how it handles fractional powers of negative inputs, so verify the intended domain when a result is missing or unexpected.

Common Mistakes and Limits

• Confusing the base and exponent: 2³ is 8, but 3² is 9. They are not interchangeable.
• Leaving out parentheses: use parentheses to show that an entire negative number is the base, as in (−2)⁴.
• Assuming every exponent means repeated multiplication: that description directly applies to positive integers. Roots and reciprocals explain fractional and negative exponents.
• Rounding too early: keep full precision in intermediate steps when comparing or combining calculations, and round the final result to the precision the task requires.
• Using a zero base with a negative exponent: 0 raised to a negative power would require division by zero and is undefined.

Very large powers may exceed the range that a calculator or computer can display, and very small values may be rounded to zero in limited-precision systems. A rounded decimal is an approximation, not always an exact representation; for instance, 1/3 has an indefinitely repeating decimal expansion.

Frequently Asked Questions

How do I calculate a number to the power of another number?
Enter the first number as the base and the second as the exponent. For a positive whole-number exponent, multiply the base by itself that many times; the calculator applies the same power rules to other supported real inputs.

What is a power function?
A power function has the form f(x) = xⁿ, where x is the input and n is a fixed exponent. More generally, xⁿ is the value of raising a base x to an exponent n.

What does a negative exponent mean?
A negative exponent means take the reciprocal of the corresponding positive power: x⁻ⁿ = 1/xⁿ. The base cannot be zero, because division by zero is undefined.

Can I raise a negative number to a fractional power?
Sometimes. A negative number raised to a fraction with an odd root, such as (−8)^(1/3), can have a real result. An even root such as (−8)^(1/2) has no real result, although it can be evaluated using complex numbers.

Why is my answer different when I use parentheses?
Because standard order of operations evaluates exponents before a leading negative sign. Thus −2⁴ means −16, while (−2)⁴ means 16. Parentheses specify whether the negative sign belongs to the base.

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in base | Base (x) | - | 2 | - | -
in exp | Exponent (n) | - | 5 | - | -
out power | Power function value (x^n) | - | base ^ exp | 6