Negative and Zero Exponents Calculator

What Are Exponents?

An exponent indicates how many times a number (the base) is multiplied by itself. For example, 2³ means 2 multiplied by itself three times: 2 × 2 × 2 = 8.

Exponents can be positive, negative, or zero. Each type has its own set of rules:

• Positive exponents: The base is multiplied by itself the number of times indicated by the exponent.
• Negative exponents: The base is reciprocated and then multiplied by itself the number of times indicated by the absolute value of the exponent.
• Zero exponents: Any non-zero number raised to the power of zero equals 1.

Negative Exponents

Negative exponents indicate the reciprocal of the base raised to the positive exponent. The general rule is:

For example, 2⁻³ equals 1 divided by 2³, which is 1/8 or 0.125.

Negative exponents are commonly used in algebra, physics, and engineering to simplify expressions and represent very small quantities.

Zero Exponents

Any non-zero number raised to the power of zero equals 1. The general rule is:

For example, 5⁰ = 1, 10⁰ = 1, and even (1/2)⁰ = 1.

This rule is particularly useful in calculus and algebra for simplifying expressions and solving equations.

Using the Calculator

Our interactive calculator makes it easy to compute negative and zero exponents. Simply enter the base and exponent values, then click "Calculate".

The calculator will display the result and show you the step-by-step calculation process.

Worked Examples

Example 1: Negative Exponent

Calculate 3⁻².

Using the negative exponent rule:

3⁻² = 1 / 3² = 1 / 9 ≈ 0.1111

Example 2: Zero Exponent

Calculate 7⁰.

Using the zero exponent rule:

7⁰ = 1