What is an exponent calculator?
An exponent calculator raises a number (the base) to a power (the exponent) and shows the result. Type the base x and the exponent y and it works out xʸ with steps. It handles negative exponents as well as decimal and fractional exponents, and it switches to scientific notation when the answer is too large or too small to show in full. It works as a free power calculator for maths homework, science and finance.
What is an exponent?
An exponent tells you how many times to multiply a number by itself. In 2⁵, 2 is the base and 5 is the exponent, also called the power or index: 2⁵ = 2 × 2 × 2 × 2 × 2 = 32. We read it as “2 to the power 5” or “2 raised to 5”. Writing numbers this way is called exponential form, or index form in Indian textbooks. Squares (x²) and cubes (x³) are the most common exponents.
How to use the exponent calculator
- Enter the base x, the number being multiplied. It can be negative or a decimal.
- Enter the exponent y. Whole numbers, negatives and decimals all work. For a fraction such as ⅔, type 0.666667, or find the root separately with the square root calculator.
- Read the answer, the step-by-step expansion, scientific notation and the reciprocal.
Exponent formula
xn = x × x × x × … × x (n times)
For a whole-number exponent this is repeated multiplication. For other exponents, calculators use the identity xy = ey × ln x, which works for any positive base and any real exponent.
Laws of exponents (exponent rules)
| Rule | Formula | Example |
|---|---|---|
| Product rule (multiplication) | xa × xb = xa+b | 2³ × 2⁴ = 2⁷ = 128 |
| Quotient rule (division) | xa ÷ xb = xa−b | 5⁶ ÷ 5⁴ = 5² = 25 |
| Power of a power | (xa)b = xab | (3²)³ = 3⁶ = 729 |
| Power of a product | (xy)a = xaya | (2 × 5)³ = 8 × 125 = 1,000 |
| Zero exponent | x0 = 1 (x ≠ 0) | 7⁰ = 1 |
| Negative exponent | x−a = 1 ÷ xa | 2⁻³ = 1/8 = 0.125 |
| Fractional exponent | xa/b = (ᵇ√x)a | 82/3 = (∛8)² = 4 |
These exponent laws let you simplify expressions with variables too: x³ × x⁵ = x⁸ and (x²y)³ = x⁶y³, whatever the values of x and y.
How to calculate exponents: worked examples
Positive whole exponent
3⁴ = 3 × 3 × 3 × 3 = 81. 2¹⁰ = 1,024, the default example above; this is why a kilobyte is sometimes counted as 1,024 bytes.
Negative exponent
A negative exponent means “one divided by”. 10⁻² = 1 ÷ 10² = 1/100 = 0.01, and 4⁻¹ = 0.25. A negative base with an even exponent is positive, (−3)² = 9, while an odd exponent keeps the sign, (−3)³ = −27. Note that −3² means −(3²) = −9; use brackets on a calculator.
Fractional and decimal exponents
An exponent of ½ is a square root: 160.5 = 4. An exponent of ⅓ is a cube root: 271/3 = 3. For 91.5, take the square root and cube it: (√9)³ = 27. A negative base with a fractional exponent, such as (−8)0.5, has no real answer, and the calculator tells you so.
Large numbers
Powers grow fast. 2⁶⁴ = 18,446,744,073,709,551,616, about 1.8447 × 10¹⁹. For huge results like 7¹⁰⁰⁰ the calculator uses logarithms to give the answer in scientific notation (about 1.25 × 10⁸⁴⁵) and tells you how many digits it has, instead of showing “Infinity”.
Fractions, decimals, huge numbers and roots
- Exponent calculator with fractions: enter the fraction as a decimal exponent (¾ = 0.75), or a fractional base such as 0.5 for ½. (½)³ = 0.125 = 1/8.
- Exponent calculator with decimals: 1.5² = 2.25 and 20.5 ≈ 1.41421; decimal bases and decimal exponents both work.
- Exponent calculator for large numbers: results above 10²¹ are shown in scientific notation, while anything smaller is shown in full with no scientific notation.
- Exponent root calculator: a root is an exponent of 1/n, so the cube root of 125 is 1251/3 = 5.
- Exponent multiplication and division: to multiply or divide powers with the same base, use the rules table above to add or subtract the exponents first, then calculate the single power here.
- Simplify an exponent expression with variables: the calculator needs numbers, but the exponent laws let you simplify x and y terms by hand, such as x⁷ ÷ x² = x⁵, and then substitute a value to check the exponent value.
Exponential formula for growth and interest
The exponential growth formula is A = P × (1 + r)ⁿ, where r is the growth rate per period and n is the number of periods. For an investment growing 1% a month, the monthly growth factor for 12 months is 1.01¹² ≈ 1.1268, and over 10 years (120 months) it is 1.01¹²⁰ ≈ 3.3004. An exponential equation such as 2ˣ = 64 is solved the other way, with logarithms: x = log 64 ÷ log 2 = 6.
So this page also works as an exponential calculator for growth and interest: enter 1 + r as the base and the number of periods as the exponent to get the growth factor, then multiply by your investment. For monthly growth over several years, use the monthly rate and the number of months. The exponential calculator formula is the same one used by banks for compound interest, and an exponent log calculator pair (this page with the log calculator) solves any exponential equation. As an exponent rules calculator check, work out 2³ × 2⁴ and 2⁷ separately here and confirm both give 128; for division, 5⁶ ÷ 5⁴ and 5² both give 25.
How to calculate an exponential value in a calculator quickly
To calculate an exponential value such as e² on a calculator, press the eˣ key (often SHIFT + ln) and type 2 to get 7.389. For exponents of any base, the calculation formula stays xʸ: type the base, the ^ key and the power. To calculate exponents quickly by hand, use the repeated squaring trick below.
How to calculate exponents without a calculator
- Repeated squaring: to find 3⁸, square 3 to get 9, square again to get 81, and once more to get 6,561. This takes 3 steps instead of 7 multiplications.
- Split the exponent: 2¹³ = 2¹⁰ × 2³ = 1,024 × 8 = 8,192.
- Powers of 10: 10ⁿ is 1 followed by n zeros, so 10⁶ = 10,00,000 (ten lakh, one million).
How to type an exponent on a calculator
The exponent symbol on a calculator is usually a caret (^) or an xʸ button. On a scientific calculator, use the xʸ, yˣ or ^ key: type the base, press ^, type the exponent and press =. For squares there is usually an x² key. On an iPhone, turn the calculator sideways to see the exponent (xʸ) button. On a basic calculator with no exponent key, multiply the base by itself repeatedly: type 3 × 3 and press = several times on many models. In Excel or Google Sheets use =POWER(2,10) or =2^10. In Python write 2**10, and in JavaScript Math.pow(2, 10). The “E” or “EXP” key is different: it enters scientific notation, so 3E4 means 3 × 10⁴.
Exponents in real life: exponential growth
Exponents describe anything that grows by a fixed percentage each period. Compound interest is the classic example: an amount P growing at r% a year becomes P × (1 + r/100)ⁿ after n years. ₹1,00,000 at 8% for 10 years grows to 1,00,000 × 1.08¹⁰ ≈ ₹2,15,892. Enter base 1.08 and exponent 10 above to check the growth factor 2.1589, or use the compound interest calculator. Population growth, bacteria doubling and radioactive decay all follow the same exponential pattern. The reverse question, “what power gives this number?”, is answered by the log calculator.
Power calculator formula: exponent calculator as a power calculator
In maths, a "power calculator" is the same as an exponent calculator: in India and elsewhere, students say "2 to the power 10" for 210. The power calculator formula is an = a × a × … × a (n times), with a−n = 1 ÷ an and a1/n = ⁿ√a. You do not need a power calculator app; this page works in any phone browser.
Exponent calculator multiplication rules
When you multiply powers with the same base, add the exponents: 2³ × 2⁴ = 2⁷ = 128. When the exponents match but the bases differ, multiply the bases: 2³ × 5³ = 10³ = 1,000. A power of a power multiplies exponents: (3²)³ = 3⁶ = 729. Use the exponent calculator for multiplication checks by computing each side.
Exponential growth calculator: monthly compounding
Exponential growth follows A = P × (1 + r)n. For an exponential growth calculator with monthly steps, use the monthly rate and the number of months. ₹10,000 growing 1% a month for 24 months is 10,000 × 1.0124 = ₹12,697. Enter base 1.01 and exponent 24 above to get the growth factor 1.2697.
Exponential regression calculator: y = abx
An exponential regression calculator fits y = abx to data. With two exact points you can solve it by hand: b = (y₂ ÷ y₁)1 ÷ (x₂ − x₁) and a = y₁ ÷ bx₁. For (1, 6) and (3, 54): b = 91/2 = 3 and a = 6 ÷ 3 = 2, so y = 2 × 3x. With more points, a spreadsheet's LOGEST or an exponential trendline does a least-squares fit.
Exponential calculator graph
The graph of y = bx passes through (0, 1). If b > 1 it rises faster and faster; if 0 < b < 1 it decays towards zero. Plot a few values from the exponent calculator (x = −2 to 5) to sketch it, or use a graphing tool for the smooth curve.
Frequently asked questions
How do you calculate exponents?
Multiply the base by itself as many times as the exponent says. 5³ = 5 × 5 × 5 = 125. For negative exponents take the reciprocal, and for fractional exponents take a root.
What is a negative exponent?
A negative exponent means the reciprocal of the positive power: x⁻ⁿ = 1 ÷ xⁿ. For example 2⁻³ = 1/8 = 0.125.
What is any number to the power 0?
Any non-zero number raised to the power 0 equals 1. 0⁰ is usually taken as 1 by convention.
How do I calculate a fractional exponent?
The denominator is the root and the numerator is the power: x^(a/b) = (b-th root of x)^a. So 8^(2/3) = (∛8)² = 2² = 4.
What is exponential form?
Exponential form writes repeated multiplication as a base and an exponent. 2 × 2 × 2 × 2 is written as 2⁴.
What are the exponent rules?
Add exponents when multiplying the same base, subtract them when dividing, multiply them for a power of a power, x⁰ = 1, and x⁻ⁿ = 1/xⁿ.
How do I type an exponent on a calculator?
Use the ^, xʸ or yˣ key: base, then the key, then the exponent, then equals. In Excel use =POWER(base, exponent) or =base^exponent.
Can this exponent calculator handle large numbers?
Yes. When the answer is too big to display, it shows the result in scientific notation using logarithms, along with the number of digits.
Is a power calculator the same as an exponent calculator?
In maths, yes: both raise a base to a power. Electrical power calculators (watts) are a different tool.
How do I multiply exponents with the same base?
Add the exponents: 5² × 5³ = 5⁵ = 3,125.
Can the exponent calculator simplify expressions with variables?
Use the laws above: x³ × x⁵ = x⁸ and (x²y)³ = x⁶y³. The exponent calculator with variables rules work for any letters; the tool itself evaluates numbers.
How does the exponent calculator handle division?
For exponent calculator division with the same base, subtract exponents: 7⁵ ÷ 7³ = 7² = 49.
Can I use the exponent calculator for fractions?
Yes. Enter the fraction as a decimal base, or raise the top and bottom separately: (3/4)² = 9/16. The exponent calculator fraction exponents such as 1/2 are entered as 0.5.
Where is the exponent key on a calculator or iPhone?
Look for xʸ, yˣ or ^. For an exponent calculator on iPhone, turn the Calculator app to landscape or open the scientific layout and use the xʸ key.
Does the exponent calculator show large numbers without scientific notation?
Results below 10²¹ are shown as ordinary numbers (to 12 significant digits). For bigger answers, the exponent calculator large numbers output switches to scientific notation, such as 2¹⁰⁰ ≈ 1.2677 × 10³⁰.
Is this exponent calculator free and online?
Yes. The exponent calculator online is free and needs no sign-up.
What is exponent?
An exponent tells you how many times to multiply the base by itself. In 4³, 3 is the exponent: 4 × 4 × 4 = 64.
Last updated 2026-09-18