Compound interest: ₹1 lakh at 8% for 10 years
FV = P × (1+r)^n = 100,000 × 1.08^10 = 100,000 × 2.1589 = ₹2,15,892. The exponent 1.08^10 = 2.1589 captures the compounding magic - over double in 10 years at 8%.
Exponent Calculator - Calculatrice en ligne gratuite
Calculate any base raised to any power - positive, negative, or fractional exponents. Powers come up everywhere: compound interest, exponential decay, scientific notation, computer storage scales.
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2^10
1,024
= 2 to the power of 10
Reciprocal
0.0009765625
2^(−10)
Square root of result
32
if result ≥ 0
Une partie du contenu est encore affichée en anglais.
Comprendre : Exponent Calculator
Exponents are the shorthand for repeated multiplication and the foundation of exponential growth - the fastest-growing mathematical pattern after factorials. Compound interest at 12% per year doubles your money in roughly 6 years, triples in 10, quadruples in 12 - each year compounding on the previous. Population growth, viral spread, radioactive decay, computer memory doubling (Moore's Law), and exponential signal decay in physics all use the same exponent mathematics. Understanding exponents is essential for Class 8-12 mathematics, JEE/NEET physics, computer science (binary powers of 2), and basic financial literacy (compounding).
This calculator handles every flavor of exponent: positive integers (2^10 = 1024), zero (any non-zero base to the 0 power = 1), negative (2^-3 = 1/8 = 0.125), fractional (8^(1/3) = 2, the cube root), and decimal (10^2.5 = 316.23). For very large results that exceed JavaScript's number precision (>10^308), the calculator falls back to scientific notation. The formula display shows the exact expression so you can verify by hand and build intuition for how exponents behave at the extremes - particularly important for students preparing for board exams and competitive tests.
Utiliser Exponent Calculator en 3 étapes
Enter the base.
Enter the exponent (integer, decimal, or negative).
Read the result.
Comment fonctionne Exponent Calculator
x^n means multiplying x by itself n times for positive integers. For fractional exponents (like x^0.5), it equals the corresponding root (square root). For negative exponents, x^−n = 1 / x^n.
Formula
Result = base ^ exponent
- x^nx multiplied by itself n times (positive int)
- x^(1/n)nth root of x
- x^−n1 / x^n
Comment Exponent Calculator obtient son résultat
Key exponent rules every student should memorise: (1) x^0 = 1 for any non-zero x. (2) x^1 = x. (3) x^m × x^n = x^(m+n) - multiplying like bases adds exponents. (4) x^m ÷ x^n = x^(m−n). (5) (x^m)^n = x^(m×n) - power of a power multiplies. (6) (xy)^n = x^n × y^n - distributes over multiplication. (7) x^(-n) = 1/x^n - negative exponents flip to reciprocal. (8) x^(1/n) = nth root of x. These eight rules are the entire toolkit.
Fractional exponents combine roots and powers: x^(m/n) = (nth root of x)^m. So 8^(2/3) = (cube root of 8)^2 = 2^2 = 4. For negative bases with fractional exponents, complications arise: even denominators produce complex numbers (since √(−4) is not real). The calculator returns NaN for these cases; odd denominators (like cube roots) work fine for negative bases.
Implementation note: JavaScript uses Math.pow() internally which is IEEE 754 floating-point - precise to about 15-17 significant digits. For very large exponents like 100^100, the result has 200+ digits which standard floating point cannot represent; you'll see infinity or scientific notation. For exact large-integer arithmetic, switch to the Big Number Calculator on this site which uses BigInt and handles arbitrary precision integers.
Exemples résolus
Binary computation: 2^10, 2^20, 2^30
2^10 = 1,024 (1 KiB). 2^20 = 1,048,576 (1 MiB). 2^30 ≈ 1.07 billion (1 GiB). Doubles every 10 powers - explains why kilobyte / megabyte / gigabyte boundaries are at these powers in binary computing.
Scientific notation: speed of light in m/s
c = 3 × 10^8 m/s. Time light takes to cross a 30 cm distance (1 ft): t = 0.30 / (3×10^8) = 10^(-9) seconds = 1 nanosecond. Exponents make these tiny and huge numbers manageable.
Quand utiliser Exponent Calculator
- Class 8-12 mathematics - laws of exponents homework and exam prep.
- JEE Main, JEE Advanced, NEET - physics formulas involving powers and roots.
- Compound interest, depreciation and growth calculations.
- Computer science - binary, octal, hexadecimal conversions involve powers of 2, 8, 16.
- Scientific notation conversions in physics and chemistry.
- Engineering - exponential decay (RC circuits, radioactive half-life).
- Finance - present value, future value computations using powers of (1+r).
- Statistics - variance and standard deviation involve squaring (power of 2).
Erreurs et pièges courants
- Confusing −2^2 with (−2)^2. The first is −(2^2) = −4; the second is 4.
- Treating x^(m+n) as x^m + x^n. It's actually x^m × x^n.
- Computing 0^0 inconsistently. Most calculators return 1; this calculator does too.
- Forgetting negative exponent rule. 2^(-3) is 1/8, not −8.
- Mixing up power and root for fractional exponents. x^(1/2) is the square root, not half of x.
- Overflow on very large exponents. Use BigInt for exact large integer work.
Tirez le meilleur de cet outil
- Memorise the 8 laws of exponents - they're the entire toolkit for simplifying expressions.
- For mental approximations: 2^10 ≈ 10^3 (1024 vs 1000). Powers of 2 grow ~10× every 3.3 exponents.
- Use scientific notation (×10^n) for very large or very small numbers - easier to compare and compute.
- For compound interest, the exponent equals the number of compounding periods, not just years.
- Pair with the log, root and scientific notation calculators on this site for related power-and-root math.
Questions sur Exponent Calculator
What is 0^0?
Mathematically debated - most calculators return 1 by convention, which is what you get here. In limits and analysis, 0^0 is indeterminate.
Can I use negative bases with fractional exponents?
Only when the denominator is odd (cube root, fifth root). Even roots of negatives give complex numbers, which this tool doesn't return.
What's the difference between e^x and exp(x)?
Same thing. e^x and exp(x) both denote the natural exponential function. e ≈ 2.71828.
How do I compute square root using exponents?
x^0.5 or x^(1/2). For nth root, use x^(1/n).
Why does 2^10 = 1024?
1024 = 2^10. That's why kilobytes are 1024 bytes (in binary terms). Powers of 2 underpin all binary computation.
What about very large exponents like 100^100?
Standard JavaScript Numbers overflow around 1.8 × 10^308. For larger results, use the Big Number Calculator with BigInt support.
Math in your browser
From simple percentages to scientific notation, statistics, geometry and big-number arithmetic - every common math problem you'd reach for a calculator for, runs in your browser with no installs. The fraction calculator preserves exact rationals, the big-number calculator uses BigInt for hundreds of digits without precision loss, and the scientific calculator's expression evaluator is a hand-written shunting-yard parser (no eval) that supports trig, log, factorial and parentheses.
If you're a student, double-check your work without paying for a graphing calculator. If you're a professional, use these tools as a sanity check on spreadsheet formulas. Every result is shown alongside its formula and inputs, so the math is always auditable.
The Exponent Calculator is part of the Math suite on Online Calculator Tools, alongside 6 related calculators. All tools share the same UI patterns, the same privacy-first rendering (nothing is sent to a server), and the same commitment to showing the formula and assumptions behind every result.