Precision Utility
Power & Exponent
Calculator
Mode
xn Powers
Mode
n√x Roots
Calculate powers, exponents and nth roots instantly. Enter a base and exponent to see the result in standard and scientific notation, or switch to root mode to find any nth root. Results update automatically as you type.
Power Mode
Result
16
Formula
24 = 16
Result
16
Scientific Notation
1.6e+1
Base
2
Exponent
4
How the power calculator works
Choose your mode at the top: Power mode or Nth Root mode. In Power mode, enter a base number and an exponent. The calculator multiplies the base by itself the number of times specified by the exponent. For example, entering base 2 and exponent 4 gives you 2 x 2 x 2 x 2 = 16.
In Nth Root mode, enter a value and a root degree. The calculator finds the number that, when raised to that power, gives you the original value. For example, the cube root (3rd root) of 27 is 3 because 3 x 3 x 3 = 27.
Results update automatically as you type. You will see the answer in both standard form and scientific notation, along with a formula breakdown showing the full expression.
Understanding powers, exponents and roots
Exponentiation is one of the fundamental operations in mathematics. A power expression has two parts: the base (the number being multiplied) and the exponent (how many times to multiply). Written as xn, it means "x multiplied by itself n times".
Key rules of exponents:
- Zero exponent: Any non-zero number raised to the power of 0 equals 1 (e.g. 50 = 1)
- Negative exponent: x-n = 1 / xn (e.g. 2-3 = 1/8 = 0.125)
- Fractional exponent: x1/n is the nth root of x (e.g. 81/3 = 2)
- Product rule: xa x xb = xa+b
- Power rule: (xa)b = xa x b
Roots are the inverse of powers. The square root of 9 is 3 because 32 = 9. The cube root of 64 is 4 because 43 = 64. This calculator handles any root degree.
Powers and exponents in a UK context
In the United Kingdom, power calculations crop up far more often than most people realise — particularly when it comes to household energy bills. Your electricity supplier charges in kilowatt-hours (kWh), which is simply a power rating raised over time. Understanding how exponents relate to energy consumption can help you make sense of your quarterly bills and identify where savings are possible.
UK electrical installations must comply with BS 7671 (the IET Wiring Regulations), where power calculations are essential for determining cable sizes, circuit breaker ratings and maximum demand. Electricians routinely use the formula P = I²R (power equals current squared times resistance) — a direct application of exponents — when designing domestic and commercial circuits to British Standards.
Powers and exponents are also a core part of the GCSE Mathematics curriculum across all UK exam boards (AQA, Edexcel and OCR). Students are expected to evaluate expressions with integer and fractional exponents, understand index laws, and apply them to real-world problems. At A-Level, exponential growth and decay models extend these concepts into population modelling, radioactive half-life calculations and compound interest — all topics examined regularly in UK sixth-form mathematics.
Worked examples for UK students and homeowners
Example 1: Immersion heater energy cost
A typical UK immersion heater is rated at 3 kW. How much energy does it use over 4 hours?
Solution: Energy (kWh) = Power × Time = 3 kW × 4 h = 12 kWh. At the current Ofgem price cap of roughly 24.5p per kWh, that costs about £2.94. While this is a multiplication rather than an exponent, the concept of "power" in physics is directly named after the mathematical operation — and compound tariff calculations do involve exponential pricing tiers.
Example 2: GCSE index law question
Simplify 23 × 25.
Solution: Using the product rule (add the exponents when the bases are equal): 23+5 = 28 = 256. This type of question appears frequently in GCSE papers from AQA, Edexcel and OCR, and is worth 1–2 marks.
Example 3: Compound interest on a UK ISA
You deposit £5,000 into a Cash ISA at 4.5% annual interest. What is it worth after 6 years with compound interest?
Solution: Future Value = £5,000 × (1.045)6 = £5,000 × 1.30226 = £6,511.30. The exponent here (6) represents the number of compounding periods — a practical use of powers that every UK saver should understand.
Frequently asked questions
What is a power or exponent?
A power (or exponent) tells you how many times to multiply a number by itself. For example, 2 raised to the power of 4 means 2 x 2 x 2 x 2 = 16. The base is the number being multiplied and the exponent is the number of times it is multiplied.
What is an nth root?
An nth root is the inverse of raising a number to a power. The nth root of a value finds the number that, when raised to the nth power, gives the original value. For example, the 3rd root of 27 is 3 because 3 x 3 x 3 = 27.
What happens when you raise a number to the power of 0?
Any non-zero number raised to the power of 0 equals 1. This is a fundamental rule of exponents. For example, 50 = 1, and 10000 = 1. The expression 00 is generally defined as 1 in most mathematical contexts.
Can you raise a number to a negative exponent?
Yes. A negative exponent means you take the reciprocal of the base raised to the positive exponent. For example, 2-3 equals 1 / (2 x 2 x 2) = 1/8 = 0.125. This calculator handles negative exponents automatically.
Can you raise a number to a fractional exponent?
Yes. A fractional exponent combines a power and a root. For example, 81/3 is the cube root of 8, which is 2. The denominator of the fraction is the root and the numerator is the power. This calculator supports decimal exponents which work the same way.
What is scientific notation?
Scientific notation expresses very large or very small numbers in a compact form: a coefficient between 1 and 10 multiplied by a power of 10. For example, 1,000,000 becomes 1.0 x 106. This calculator shows every result in scientific notation alongside the standard form.