Enter any number and a negative exponent into the calculator. The calculator will display the value of the number raised to the negative exponent.

Negative Exponent Formula

The following formula can be used to calculate the value of a number raised to a negative exponent. 

X^-Y = 1/X^Y
  • Where X is the number being raised to
  • Y is the exponent

Negative Exponent Definition

A negative exponent is equal to the inverse of the function raised to the positive value of that exponent.

Examples

The following examples show the process of calculating a negative exponent value.

  1. 5 ^ -2 = 1/5^2 = 1/25
  2. 4^ -3 = 1/4^3 = 1/48
  3. 10^-3 = 1/10^3 = 1/1000
  4. 2 ^ -5 = 1/2^5 = 1/32
  5. 1 ^ -1 = 1/1^1 = 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.

How do you calculate a number raised to a negative exponent without a calculator?
To calculate a number raised to a negative exponent without a calculator, first convert the negative exponent to a positive one by taking its absolute value. Then, raise the number to this positive exponent. Finally, take the reciprocal of this result to get the final answer.

Can zero be raised to a negative exponent?
No, zero cannot be raised to a negative exponent. This is because raising zero to any negative exponent would imply division by zero, which is undefined in mathematics.

Are there any practical applications of negative exponents in real life?
Yes, negative exponents are used in various fields such as physics, engineering, and finance to represent quantities that decrease exponentially, calculate decay rates, model inverse relationships, and simplify expressions involving reciprocals of quantities.