Exponent calculator with steps

This exponent calculator works out any power exactly, whether the exponent is a whole number, a negative number or a fraction. Type a base and an exponent, such as 2 and 10, and it gives the answer, 1,024, with the working. It also simplifies roots, such as √72 = 6√2, and shows each exponent rule applied to your own numbers.

Exponents are also called powers or indices, and the exponent is the small raised number: in 2¹⁰, 2 is the base and 10 is the exponent. The calculator opens on 2¹⁰.

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Exponent Calculator

Work out powers and roots and apply the index laws

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How to use the exponent calculator

1. Under What to do, choose Power, Root or Index laws.
2. For Power, type the Base and the Power. Either can be a whole number, a decimal or a fraction, so a power of 2/3 or −3/4 works.
3. For Root, type the number and Which root: 2 for a square root, 3 for a cube root, up to 100.
4. For Index laws, pick a law, then type the base and the powers m and n.
5. Read the answer and the working. A fraction answer also comes as a decimal, and a root that does not come out exactly is given as a simplified surd and a decimal.

Answers are exact. 2¹⁰⁰ comes out in full, all 31 digits, and an answer longer than 40 digits is shown in standard form with its digit count. When there is no real answer, such as the square root of a negative number, the calculator says why. For practice, Practice and help sets questions on powers, fraction exponents and the exponent rules, with hints and worked solutions.

Powers worth knowing

These come up so often that knowing them saves time, especially without a calculator.

Every kind of exponent, with examples

Each row can be typed into Power mode to check it.

Example 1: a negative exponent

Work out 3⁻². A negative exponent means one over the positive power. It does not make the answer negative:

The calculator gives 1/9 and the decimal 0.1111111111.

Example 2: a fraction exponent

Work out 25^(3/2). In a fraction exponent, the bottom number is a root and the top number is a power. Take the root first, because it keeps the numbers small:

This is what people mean by a fraction exponent calculator or a rational exponent calculator. Type 25 as the base and 3/2 as the power.

Example 3: a negative fraction exponent

Work out 16^(−3/4). Deal with the minus sign first, then the fraction:

Example 4: growth over time

An amount grows by 5% a year for 10 years. Each year multiplies it by 1.05, so after 10 years it has been multiplied by 1.05¹⁰. The calculator gives this exactly as a fraction and as the decimal 1.62889462677744140625. So $1,000 grows to $1,628.89. Repeated percentage change is one of the most common uses of exponents outside a maths class.

Example 5: halving again and again

A quantity halves 5 times, as a radioactive sample does over 5 half-lives. The fraction left is 0.5⁵, or (1/2)⁵:

So 3.125% is left. Type 1/2 as the base and 5 as the power. For real decay problems with any time, use the Half-Life Calculator.

How many digits does a big power have?

The number of digits in a whole number answer is one more than the whole number part of its logarithm. For 2¹⁰⁰, log₁₀(2¹⁰⁰) = 100 × 0.30103 = 30.1, so it has 31 digits, which matches the calculator. The same idea gives 3⁵⁰ 24 digits. The Logarithm Calculator works out the log for any base.

Roots: square, cube and nth roots

A root undoes a power: the cube root of 8 is 2 because 2³ = 8. In Root mode the calculator writes the number as a product of primes and takes out every complete group, which simplifies the root as a surd:

For √72: 72 = 2³ × 3², so one pair of 2s and one pair of 3s come out as 2 × 3 = 6, leaving one 2 inside. A negative number has no real square root, or any even root, so the calculator refuses those. Odd roots of negatives are fine: the cube root of −8 is −2.

Exponent rules with your own numbers

Index laws mode applies each exponent rule to the numbers you choose, shows the general rule, then your numbers, then the answer. Small whole powers also appear as tiles you can count.

Our exponent rules guide goes through each law in depth. The rules only work when the bases are the same. 2³ × 3⁴ cannot be combined into one power. Try one in the course, then press Mark to check it:

How to put an exponent in a calculator

On a handheld scientific calculator, the exponent button is usually marked ^, xʸ or yˣ. Type the base, press the exponent button, then type the exponent. For a fraction exponent, put it in brackets: 25^(3/2), not 25^3/2, which most calculators read as 25³ ÷ 2.

Watch negative bases. Calculators follow the order of operations, so typing −2^4 gives −16, the negative of 2⁴. To raise −2 to the power 4, type (−2)^4, which gives 16. In this exponent calculator the base box holds the whole base, so typing −2 as the base and 4 as the power gives 16.

Common mistakes

• Multiplying the base by the exponent. 2³ is 2 × 2 × 2 = 8, not 2 × 3 = 6.
• Making a negative exponent negative. 3⁻² is 1/9, a small positive number, not −9.
• Missing brackets on a negative base. (−2)⁴ = 16 but −2⁴ = −16.
• Using the rules on different bases. 2³ × 3² is 8 × 9 = 72. It is not 6⁵.
• Spreading a power over a sum. (a + b)² is not a² + b². Expand the brackets instead.
• Taking the power before the root with big numbers. For 64^(2/3), the cube root first gives 4² = 16. Squaring first means finding the cube root of 4,096.

Practise exponents in a short timed paper

Exponents run through Pre-Algebra & Algebra 1 and Geometry, Algebra 2 & SAT Math practice, and through GCSE Maths Higher in the UK, where they are called indices. Each daily paper is a short timed paper of 8 questions worth 25 to 35 marks, and the papers mix topics. For very large and very small numbers, the Scientific Notation Calculator and the scientific notation guide take it further.

Read next

Maths · AlgebraExponent rules: all 7 laws of exponents with examplesAll the exponent rules in one chart: multiplying, dividing, powers of powers, zero, negative and fractional exponents, with worked examples and practice.