In mathematics, an exponent (or power) indicates how many times a base number is multiplied by itself. It is usually written as a small number to the right and above the base number (e.g., xⁿ). If you have 5³, it means 5 × 5 × 5.
Key Components
Base (x): The number that is being multiplied.
Exponent (n): The number of times the base is used as a factor.
Power: The result of the entire operation.
How to Use This Exponent Calculator
This tool allows you to quickly solve equations involving indices. Simply enter your base and your exponent (positive or negative) to find the result. This is particularly useful for scientific notation, compound interest formulas, and algebraic expressions.
Common Rules of Exponents
Rule Name
Rule Formula
Example
Zero Exponent
x⁰ = 1
8⁰ = 1
Negative Exponent
x⁻ⁿ = 1/xⁿ
2⁻³ = 1/8
Product Rule
xᵃ · xᵇ = xᵃ⁺ᵇ
2² · 2³ = 2⁵
Calculation Examples
Example 1: Positive Exponent
Calculate 4 to the power of 3 (4³):
4 × 4 × 4 = 64.
Example 2: Negative Exponent
Calculate 10 to the power of -2 (10⁻²):
1 / (10 × 10) = 1/100 = 0.01.
function calculatePower() {
var baseInput = document.getElementById('calcBase').value;
var exponentInput = document.getElementById('calcExponent').value;
var resultContainer = document.getElementById('calcResultContainer');
var display = document.getElementById('calcDisplay');
var expanded = document.getElementById('calcExpanded');
if (baseInput === "" || exponentInput === "") {
alert("Please enter both a base and an exponent.");
return;
}
var b = parseFloat(baseInput);
var n = parseFloat(exponentInput);
if (isNaN(b) || isNaN(n)) {
alert("Please enter valid numeric values.");
return;
}
var result = Math.pow(b, n);
// Handle display formatting
var resultString = "";
if (Math.abs(result) > 9999999 || (Math.abs(result) < 0.000001 && result !== 0)) {
resultString = result.toExponential(6);
} else {
resultString = result.toLocaleString(undefined, { maximumFractionDigits: 10 });
}
display.innerHTML = b + "" + n + " = " + resultString;
// Detailed explanation
var explanation = "";
if (n === 0) {
explanation = "Any non-zero number raised to the power of 0 is always 1.";
} else if (n === 1) {
explanation = "Any number raised to the power of 1 remains the same.";
} else if (n < 0) {
explanation = "A negative exponent means the reciprocal of the base raised to the positive power: 1 / (" + b + "" + Math.abs(n) + ").";
} else if (Number.isInteger(n) && n > 1 && n <= 20) {
explanation = b + " multiplied by itself " + n + " times.";
} else {
explanation = "The base " + b + " is raised to the power of " + n + ".";
}
expanded.innerText = explanation;
resultContainer.style.display = "block";
}