Comprehensive Calculator Guide
Raising a number to a power multiplies it by itself that many times: 2 to the power 10 is 1,024. Negative and fractional exponents work too: 10⁻³ = 0.001 and 16^0.5 = 4. Enter the base and exponent to see the result instantly.
Zero, negative and fractional exponents
Any non-zero base to the power 0 is 1. A negative exponent means the reciprocal: a⁻ⁿ = 1 ÷ aⁿ, so 2⁻² = 0.25. A fractional exponent is a root: x^0.5 is the square root, x^(1/3) the cube root, and x^(m/n) the nth root raised to m.
A negative base with a fractional exponent usually has no real result (no real number squares to −4), so the calculator shows a message. Odd roots of negatives exist: take the root of the positive value and add the minus sign, ∛(−8) = −2.
Laws of exponents and growth
Same base: multiply by adding exponents, divide by subtracting them; a power of a power multiplies them: (2³)² = 2⁶ = 64. Compound growth is exponents in action: 5% a year for 10 years multiplies a sum by 1.05¹⁰ = 1.6289, so SAR 10,000 becomes about SAR 16,289.
How to Use
- 01Enter the base.
- 02Enter the exponent: positive, negative, or fractional such as 0.5.
- 03Read the result; for an nth root, use 1/n as the exponent.
Formula Used
aⁿ = a × a × … × a (n times) | a⁻ⁿ = 1 ÷ aⁿ | a^(1/n) = nth root of aPractical Examples
Example 1: whole exponent
2¹⁰ = 1,024, which is why a binary kilobyte is 1,024 bytes.
Example 2: negative exponent
10⁻³ = 0.001, one thousandth, the meaning of "milli".
Example 3: root and growth
16^0.5 = 4; 1.05¹⁰ = 1.6289, so SAR 10,000 at 5% a year becomes about SAR 16,289.
Important Tips
- On paper −2² is −4 while (−2)² is 4; here the base is taken whole, so base −2 with exponent 2 gives 4.
- A negative exponent makes a reciprocal, not a negative number.
Common Mistakes to Avoid
- Multiplying the base by the exponent: 2⁵ is 32, not 10.
- Adding exponents for different bases.
Frequently Asked Questions
- How do I work out a negative exponent?
- Take the reciprocal of the positive power: 5⁻² = 1 ÷ 25 = 0.04.
- What is any number to the power 0?
- 1, for any non-zero base. 0⁰ is left undefined here.
- How do fractional exponents work?
- 1/n is the nth root: 81^0.25 = 3.
- How do exponents give compound growth?
- Multiply by (1 + rate) to the power of the number of periods: 1.05¹⁰ for 5% over ten years.