Exponent Calculator

A base of 2 with an exponent of 10 produces 1,024; changing the exponent to -3 produces 0.125. The exponent calculator accepts signed or decimal values, then presents the power of a number in ordinary and scientific notation. It is a numeric tool, so an exponential expression containing variables is not simplified.

Read the operation before choosing a law

For a positive whole-number exponent, 3⁴ means 3 × 3 × 3 × 3. Three is the base and four tells how many factors are used. Exponents are compact notation, but the shortcut changes with the operation around them. The rules of exponents for multiplication cannot be copied into an ordinary sum.

Addition keeps unlike powers separate

Adding exponents is not what happens in 2² + 2³. Evaluate the terms first and the answer is 4 + 8 = 12, not 2⁵. Adding exponential expressions can be shortened only when the terms are alike: 3² + 3² = 2 × 3². Subtracting exponents belongs to division of powers with the same nonzero base, not subtraction of the terms. For example, 5³ - 5² may be factored as 5²(5 - 1), but the powers are not simply subtracted.

Multiplication and division have their own shortcut

When multiplying powers with the same base, add the exponents: 2³ × 2⁴ = 2⁷. Multiplying exponents applies to a power raised to another power, such as (2³)⁴ = 2¹². Dividing exponential expressions with the same nonzero base subtracts the exponents: 7⁵ / 7² = 7³. If only the exponent matches, 2³ × 5³ = (2 × 5)³.

For 2³ × 3², neither condition is present. Calculate each part and multiply 8 by 9. Keeping the bases separate prevents a common error in multiplying exponential expressions.

Negative powers, roots and boundary cases

A negative exponent takes a reciprocal: 5⁻² = 1/5² = 0.04. A fractional exponent represents a root, as in 81^0.5 = 9. The calculator rejects a fractional exponent with a negative base because a decimal input does not reliably identify the odd-denominator fractions that can have a real result. Zero to a negative power is also rejected because it would divide by zero.

Enter numbers, not expressions: use 0.5 instead of 1/2 and -2 instead of (-2). In English number format, 1,234 is a grouped integer and 1.234 is a decimal. Scientific input such as 1e-3 means 0.001.

Checks that reveal a wrong setup

• 2¹⁰ = 1,024, a repeated product.
• 10⁻³ = 0.001, the reciprocal of 10³.
• (-2)³ = -8, while (-2)² = 4.
• -2² = -4 because the minus sign is outside the powered base.

The tool uses 1 for 0⁰, matching the convention used in combinatorics; a calculus limit containing 0⁰ still needs separate analysis. For integer bases and integer exponents from 0 to 10,000, BigInt preserves the full result within the browser's numeric range. Other calculations use floating-point arithmetic, so long decimal inputs and their results may be rounded.

An exponent calculation that overflows is not displayed as infinity. A value too small for the numeric range is not silently shown as zero either. In both cases the page warns you. Scientific notation remains useful for checking scale, while the main answer preserves an exact integer when that result can be computed safely.