Exponent Calculator Guide: Powers, Negative Exponents and Rules

An exponent calculator helps evaluate powers such as 2³, 5², or 10⁻². Exponents provide a compact way to express repeated multiplication and are widely used in algebra, science, engineering, and computing.

What is an exponent?

In the expression aⁿ, a is the base and n is the exponent. For a positive whole-number exponent, the expression means multiplying the base by itself n times. For example, 3⁴ = 3 × 3 × 3 × 3 = 81.

How to use an exponent calculator

1. Open the Exponent Calculator.
2. Enter the base number.
3. Enter the exponent or power.
4. Calculate and check the result.
5. For negative bases or fractional exponents, check whether the calculator supports the expression in the real or complex number system.

Important exponent rules

Rule	Formula	Example
Product of powers	aᵐ × aⁿ = aᵐ⁺ⁿ	2² × 2³ = 2⁵ = 32
Quotient of powers	aᵐ / aⁿ = aᵐ⁻ⁿ	5⁴ / 5² = 25
Power of a power	(aᵐ)ⁿ = aᵐⁿ	(2³)² = 64
Zero exponent	a⁰ = 1, a ≠ 0	7⁰ = 1
Negative exponent	a⁻ⁿ = 1/aⁿ, a ≠ 0	2⁻³ = 1/8

Fractional exponents and roots

A fractional exponent can represent a root. For positive a, a¹ᐟ² = √a and a¹ᐟ³ = ∛a. For example, 16¹ᐟ² = 4 and 27¹ᐟ³ = 3. Not all combinations of negative bases and fractional exponents produce real-number results.

Worked examples

4³ = 64, because 4 × 4 × 4 = 64. 10⁻² = 0.01, because 1/10² = 1/100. (−3)² = 9, because a negative number multiplied by itself is positive.

Negative bases and parentheses

Parentheses matter. (−2)² = 4, but −2² = −4 under the usual order of operations, because the exponent applies to 2 before the leading negative sign.

Common mistakes

• Multiplying a base by its exponent instead of raising it to a power.
• Assuming a negative exponent always produces a negative number.
• Ignoring parentheses around a negative base.
• Assuming 0⁰ has a universally agreed value in every mathematical context.

Frequently asked questions

What is 2 to the power of 5?

32.

What does a power of zero mean?

Any nonzero base raised to the power zero equals 1.

How do I calculate a negative exponent?

For a nonzero base, calculate the corresponding positive power and take its reciprocal.

Is squaring the same as multiplying by two?

No. Squaring means multiplying a number by itself: 6² = 36, while 6 × 2 = 12.

Try the Exponent Calculator to check powers and exponent expressions.