Exponent Calculator

Calculate exponents, powers, fractional exponents, negative exponents, and scientific notation with our free exponent calculator

Available Calculators

What is an Exponent?

An exponent (also called a power) represents how many times a number (the base) is multiplied by itself. For example, 2^3 means 2 × 2 × 2 = 8. Exponents are fundamental in mathematics, science, engineering, and finance for representing growth, decay, and large numbers.

Exponent Rules

Understanding exponent rules helps simplify complex calculations. Key rules include: multiplying powers with the same base (add exponents), dividing powers (subtract exponents), power of a power (multiply exponents), and negative exponents (take reciprocal).

Base to Power Formula

The basic exponent formula is:

b^e = b × b × ... × b (e times)

where b = base and e = exponent

Negative Exponent Formula

A negative exponent means taking the reciprocal:

b^-e = (1 ÷ b^e)

Examples of Exponent Calculations

Here are several everyday situations that show how easy it is to use our exponent calculator.

Example 1: UK Savings Account Interest

You invest £1,000 in a UK savings account at 5% annual interest, compounded annually. Calculate the value after 10 years.

You can use our calculator by entering:

What is 1000 × (1.05)^10?

The calculator returns: £1,628.89

Calculate 1.05^10 = 1.62889
Multiply: 1000 × 1.62889 = £1,628.89

The formula used is:

1000 × 1.05^10 = 1628.89

Example 2: UK City Population Growth

Manchester's population doubles every 20 years. If it starts with 50,000 people, what will it be after 60 years?

You can use our calculator by entering:

What is 50000 × 2^3?

The calculator returns: 400,000 people

Calculate 2^3 = 8
Multiply: 50000 × 8 = 400,000

The formula used is:

50000 × 2^3 = 400000

Example 3: UK Building Volume

A cube-shaped storage unit in London has a side length of 5 metres. Calculate its volume.

You can use our calculator by entering:

What is 5^3?

The calculator returns: 125 m³

5^3 = 5 × 5 × 5
5 × 5 = 25
25 × 5 = 125 m³

The formula used is:

5^3 = 125

Example 4: Power of Power

Calculate (2^3)^2 using the power of power rule.

You can use our calculator by entering:

What is (2^3)^2?

The calculator returns: 64

First calculate 2^3 = 8
Then (8)^2 = 64
Or use rule: (2^3)^2 = 2^(3×2) = 2^6 = 64

The formula used is:

(2^3)^2 = 2^6 = 64

Example 5: Cube Root

Find the cube root of 27 using fractional exponents.

You can use our calculator by entering:

What is 27^(1/3)?

The calculator returns: 3

27^(1/3) is the cube root of 27
3 × 3 × 3 = 27
Therefore: 27^(1/3) = 3

The formula used is:

27^(1 ÷ 3) = 3

Example 6: Negative Exponent

Calculate 2 raised to the power of -3.

You can use our calculator by entering:

What is 2^-3?

The calculator returns: 0.125

2^-3 = 1/(2^3)
2^3 = 8
1/8 = 0.125

The formula used is:

2^-3 = (1 ÷ 2^3) = (1 ÷ 8) = 0.125

Example 7: UK Population in Scientific Notation

The population of London is approximately 9,000,000. Convert to scientific notation.

You can use our calculator by entering:

Convert 9000000 to scientific notation

The calculator returns: 9.0 × 10^6

Move decimal point 6 places to the left
Coefficient: 9.0
Exponent: 6
Result: 9.0 × 10^6

The formula used is:

9000000 = 9.0 × 10^6

Example 8: Large Number

Calculate 10^8 (one hundred million).

You can use our calculator by entering:

What is 10^8?

The calculator returns: 100,000,000

10^8 = 10 × 10 × 10 × 10 × 10 × 10 × 10 × 10
Result: 100,000,000

The formula used is:

10^8 = 100000000

Example 9: Square Root as Exponent

Calculate the square root of 16 using fractional exponents.

You can use our calculator by entering:

What is 16^(1/2)?

The calculator returns: 4

16^(1/2) is the square root of 16
4 × 4 = 16
Therefore: 16^(1/2) = 4

The formula used is:

16^(1 ÷ 2) = √(16) = 4

Example 10: UK Investment Growth

A UK investment doubles every 8 years. If you start with £1,000, how much will you have after 24 years?

You can use our calculator by entering:

What is 1000 × 2^3?

The calculator returns: £8,000

Calculate 2^3 = 8
Multiply: 1000 × 0.125 = 125 grams

The formula used is:

1000 × 2^3 = 8000

Summary

These examples show how our exponent calculator can handle:

  • •Basic exponentiation (2^3, 5^4, etc.)
  • •Power of power calculations ((2^3)^2)
  • •Fractional exponents (8^(1/3) = cube root)
  • •Negative exponents and scientific notation

You can adapt any real-life situation involving exponents to one of these patterns and let the calculator do the work for you.

How to Use

  1. Select the type of exponent calculation you need (base to power, power of power, fractional exponent, negative exponent, or scientific notation).
  2. Enter the required values in the input fields. The calculator will automatically update results in real-time.
  3. View the result and step-by-step calculation breakdown with formulas displayed using mathematical notation.

Frequently asked questions

How do I calculate exponents?

To calculate an exponent, raise the base to the power of the exponent. For example, 2^3 = 2 × 2 × 2 = 8. For larger exponents, use the calculator to avoid manual multiplication.

What is a negative exponent?

A negative exponent means you take the reciprocal of the base raised to the positive exponent. For example, 2^-3 = 1/(2^3) = 1/8 = 0.125.

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About this tool

Published by Online Tools Center

Last updated:

Check the units, assumptions and rounding before using a result. Health and financial estimates are educational and do not replace individual professional advice.

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