Exponent Negative Calculator

What is a Negative Exponent?

A negative exponent indicates the reciprocal of a number raised to a positive exponent. In other words, a number with a negative exponent is equal to 1 divided by that number raised to the positive exponent.

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

How to Calculate Negative Exponents

Calculating negative exponents involves converting the negative exponent to a positive exponent and taking the reciprocal of the result. Here's a step-by-step guide:

1. Identify the base and the negative exponent.
2. Convert the negative exponent to a positive exponent.
3. Calculate the base raised to the positive exponent.
4. Take the reciprocal of the result.

For example, to calculate 3⁻²:

1. Identify the base (3) and the negative exponent (-2).
2. Convert the negative exponent to positive: 3².
3. Calculate 3 raised to the power of 2: 9.
4. Take the reciprocal of 9: 1/9 or approximately 0.111.

Examples of Negative Exponents

Here are some examples of negative exponents and their calculations:

• 5⁻¹ = 1/5 = 0.2
• 4⁻² = 1/16 = 0.0625
• 10⁻³ = 1/1000 = 0.001
• 2⁻⁴ = 1/16 = 0.0625

These examples demonstrate how negative exponents can be converted to positive exponents and then calculated as reciprocals.

Negative Exponent Rules

There are several rules for working with negative exponents:

1. a⁻ⁿ = 1 / aⁿ
2. a⁻ⁿ = (1/a)ⁿ
3. a⁻ⁿ × aᵐ = a⁽ⁿ⁺ᵐ⁾
4. a⁻ⁿ / aᵐ = a⁽ⁿ⁻ᵐ⁾
5. (a⁻ⁿ)ᵐ = a⁽⁻ⁿᵐ⁾

These rules help simplify calculations involving negative exponents and make them easier to understand.

Negative Exponent Calculator

Use the calculator in the sidebar to quickly calculate negative exponents. Simply enter the base and the negative exponent, then click "Calculate" to see the result.