1. What is a Negative Exponent?

A negative exponent represents the reciprocal of the base raised to the absolute value of the exponent. It's a mathematical operation that shows how many times to divide by the number rather than multiply.

2. How Does the Calculator Work?

The calculator uses the negative exponent formula:

Where:

• \( a \) — Base value (cannot be zero)
• \( b \) — Exponent value

Explanation: The negative exponent indicates the reciprocal of the positive exponent. For example, 2⁻³ = 1/2³ = 1/8 = 0.125.

3. Importance of Negative Exponents

Details: Negative exponents are essential in scientific notation, exponential decay calculations, and when working with very small numbers in fields like physics, chemistry, and engineering.

4. Using the Calculator

Tips: Enter any non-zero base value and any exponent value. The calculator will compute the result and show the step-by-step calculation.

5. Frequently Asked Questions (FAQ)

Q1: Can the base be zero?
A: No, zero to a negative power is undefined because it would require division by zero.

Q2: What if the exponent is not an integer?
A: The calculator works with any real number exponent, including fractions and decimals.

Q3: How are negative exponents used in real life?
A: They're used in scientific notation (e.g., 5.97 × 10²⁴ kg), radioactive decay calculations, and when working with very small measurements.

Q4: What's the difference between negative exponents and negative bases?
A: A negative exponent means take the reciprocal, while a negative base means the number itself is negative (e.g., (-2)⁻³ = -0.125).

Q5: Can negative exponents result in positive numbers?
A: Yes, if the base is positive, the result will always be positive regardless of the exponent's sign.