An exponent, often referred to as a "power," represents how many times a base number is multiplied by itself. In the expression xⁿ, x is the base and n is the exponent.
The Basic Formula
The standard notation is xⁿ = x × x × … × x (repeated n times). For example:
2³: 2 × 2 × 2 = 8
5²: 5 × 5 = 25
10⁴: 10 × 10 × 10 × 10 = 10,000
Key Rules of Exponents
Rule Name
Mathematical Rule
Example
Zero Exponent
x⁰ = 1
7⁰ = 1
Negative Exponent
x⁻ⁿ = 1 / xⁿ
2⁻² = 1/4 = 0.25
Product Rule
xᵃ × xᵇ = xᵃ⁺ᵇ
2² × 2³ = 2⁵ (32)
Quotient Rule
xᵃ / xᵇ = xᵃ⁻ᵇ
5⁴ / 5² = 5² (25)
When to Use a Power Calculator
While calculating 3² is simple mental math, exponents grow exponentially (hence the name). Calculating large bases with high exponents, or negative and fractional exponents, becomes complex. This tool helps in:
Scientific Research: Measuring bacterial growth or radioactive decay.
Computing: Measuring bits, bytes, and memory capacity (powers of 2).
Physics: Calculating gravitational force or light intensity.
function calculateExponent() {
var base = document.getElementById("baseValue").value;
var exponent = document.getElementById("exponentValue").value;
var resultBox = document.getElementById("resultDisplay");
var mathLine = document.getElementById("mathExpression");
var resultLine = document.getElementById("finalResult");
// Validation
if (base === "" || exponent === "") {
alert("Please enter both a base and an exponent.");
return;
}
var numBase = parseFloat(base);
var numExp = parseFloat(exponent);
if (isNaN(numBase) || isNaN(numExp)) {
alert("Please enter valid numeric values.");
return;
}
// Perform Calculation
var result = Math.pow(numBase, numExp);
// Logic to format result
var formattedResult;
if (Math.abs(result) > 1000000 || (Math.abs(result) < 0.0001 && result !== 0)) {
formattedResult = result.toExponential(6);
} else {
// If it's a whole number, don't show decimals, otherwise show up to 8
formattedResult = Number.isInteger(result) ? result.toLocaleString() : parseFloat(result.toFixed(8)).toLocaleString();
}
// Display
mathLine.innerHTML = numBase + " raised to the power of " + numExp;
resultLine.innerText = formattedResult;
resultBox.style.display = "block";
// Handle infinity/very large numbers
if (!isFinite(result)) {
resultLine.innerText = "Value too large to display";
resultLine.style.fontSize = "20px";
} else {
resultLine.style.fontSize = "28px";
}
}