In mathematics, a negative exponent indicates that a number should be divided by itself a certain number of times. Specifically, raising a number to a negative exponent is equivalent to taking the reciprocal of the number raised to the positive version of that exponent.
The general formula for a negative exponent is:
a-n = 1 / an
Where:
a is the base number (any non-zero real number).
n is a positive exponent. The original exponent is -n.
How the Calculator Works
This calculator takes two inputs:
Base Number: The number that will be raised to a power.
Negative Exponent: The power to which the base number will be raised. This value *must* be negative for the calculation as intended.
The calculator then applies the rule of negative exponents. If you input a base number 'b' and a negative exponent '-e' (where 'e' is a positive number), the calculation performed is:
b-e = 1 / be
The result will be a fraction or a decimal representing this value.
Example Calculation
Let's say we want to calculate 2-3.
Base Number = 2
Negative Exponent = -3
Using the formula:
2-3 = 1 / 23
First, we calculate 23:
23 = 2 * 2 * 2 = 8
Now, we find the reciprocal:
1 / 8 = 0.125
So, 2-3 equals 0.125.
Use Cases
Understanding negative powers is crucial in various fields:
Scientific Notation: Used to represent very small numbers (e.g., 3.5 x 10-4).
Physics and Engineering: Dealing with quantities like small resistances, capacitance, or inverse relationships.
Computer Science: Algorithms and data structures might involve inverse relationships or rates.
Calculus: Derivatives and integrals often involve powers, including negative ones.
function calculateNegativePower() {
var baseInput = document.getElementById("base");
var exponentInput = document.getElementById("exponent");
var resultDiv = document.getElementById("result");
var base = parseFloat(baseInput.value);
var exponent = parseFloat(exponentInput.value);
if (isNaN(base) || isNaN(exponent)) {
resultDiv.innerHTML = "Please enter valid numbers for both base and exponent.";
return;
}
if (base === 0 && exponent = 0) {
resultDiv.innerHTML = "Please enter a negative number for the exponent.";
return;
}
// Calculate the positive exponent first
var positiveExponent = -exponent; // Make the exponent positive for Math.pow
var denominator = Math.pow(base, positiveExponent);
// Calculate the final result: 1 / (base ^ positiveExponent)
var finalResult = 1 / denominator;
resultDiv.innerHTML = base + "" + exponent + " = " + finalResult.toFixed(8); // Displaying with a few decimal places
}