Negative Exponent Calculator

Formula

To calculate the value of a number raised to a negative exponent:

\[ X^{-Y} = \frac{1}{X^Y} \]

Where:

\( X \) is the base number
\( Y \) is the exponent

What is a Negative Exponent?

A negative exponent represents the reciprocal of the base raised to the positive value of the exponent. It is a way to express division operations as exponentiation to a negative power.

Examples

Here are some examples of calculating negative exponents:

\[ 5^{-2} = \frac{1}{5^2} = \frac{1}{25} \]
\[ 4^{-3} = \frac{1}{4^3} = \frac{1}{64} \]
\[ 10^{-3} = \frac{1}{10^3} = \frac{1}{1000} \]
\[ 2^{-5} = \frac{1}{2^5} = \frac{1}{32} \]
\[ 1^{-1} = \frac{1}{1^1} = \frac{1}{1} = 1 \]

FAQ

What does raising a number to a negative exponent represent?

Raising a number to a negative exponent represents taking the reciprocal of the number raised to the absolute value of that exponent. It's a way to express division operations as exponentiation to a negative power.