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Exponent & Root calculator →

Exponent & Root guide

The Exponent & Root Calculator handles positive powers, negative powers, and fractional exponents (roots). It includes a dynamic table generator so you can quickly view the powers of a base up to 100.

Worked examples

Calculate a standard power (2 to the power of 5)

  1. Enter 2 as the Base.
  2. Enter 5 as the Exponent.
  3. Click Calculate.
Result: 2^5 = 32

This means multiplying 2 by itself 5 times: 2 × 2 × 2 × 2 × 2 = 32.

Calculate a negative exponent (2 to the power of -3)

  1. Enter 2 as the Base.
  2. Enter -3 as the Exponent (you can use the (-) button).
  3. Click Calculate.
Result: 2^-3 = 0.125

A negative exponent means taking the reciprocal. 2^-3 is the same as 1 / (2^3) = 1/8 = 0.125.

Evaluate a fractional exponent (16 to the power of 3/4)

  1. Enter 16 as the Base.
  2. Enter 3/4 as the Exponent.
  3. Click Calculate.
Result: 16^(3/4) = 8

The denominator (4) means take the 4th root, and the numerator (3) means cube the result. The 4th root of 16 is 2, and 2^3 = 8.

Tips

  • •Use the Table Generator button to see all powers of a base (e.g., 2^1 through 2^30).
  • •Always wrap negative bases in parentheses (e.g., (-2)^2) to avoid calculation errors.
  • •Results too large for standard display are automatically converted to scientific notation.

Frequently asked questions

What is a negative exponent?
A negative exponent tells you to take the reciprocal of the base. For example, x^-n = 1 / (x^n).
Why is any number to the power of 0 equal to 1?
It is a mathematical rule that keeps the pattern of exponents consistent. As exponents decrease (2^3, 2^2, 2^1), the result is divided by the base each time. So 2^0 = 1.
What does a fractional exponent mean?
A fractional exponent combines powers and roots. The denominator is the root, and the numerator is the power. For example, 8^(1/3) is the cube root of 8.
Why do I get an error for a negative base with a fractional exponent?
Taking an even root (like a square root) of a negative number results in an imaginary number. Standard calculators only handle real numbers, so this throws an error.
What is scientific notation?
It is a way to write very large or very small numbers compactly, like 1.5 × 10^8. The calculator automatically switches to this format when the result is over 1,000,000 or under 0.0001.
How do I calculate a square root using exponents?
Use a fractional exponent of 1/2. For example, 25^(1/2) = 5.
How do I calculate a cube root using exponents?
Use a fractional exponent of 1/3. For example, 27^(1/3) = 3.
What is the difference between 2^3 and 3^2?
2^3 means 2 × 2 × 2 = 8. 3^2 means 3 × 3 = 9. The base and the exponent are different.
Can the exponent be a decimal?
Yes. For example, 9^0.5 is exactly the same as 9^(1/2), which is 3.
What happens if the result is Infinity?
If a number is raised to a massive power that exceeds the limits of JavaScript numbers (about 1.7 × 10^308), the calculator will show an Infinity error.
What is the difference between a power and an exponent?
The exponent is the small number written above and to the right. The power is the entire expression (base + exponent). However, people often use the terms interchangeably.
Can I use parentheses in the input?
Yes. You can enter expressions like (1/2) or -(3) to ensure the math evaluates correctly.
What is the Table Generator?
It is a built-in tool that instantly lists the first 100 powers of any base, saving you from calculating them one by one.
Why is 0^0 undefined?
It is mathematically an indeterminate form. Some branches of math define it as 1, but the calculator will typically throw an error or return NaN (Not a Number).
What is the difference between exponentiation and multiplication?
Multiplication is repeated addition (3 × 4 = 3+3+3+3). Exponentiation is repeated multiplication (3^4 = 3 × 3 × 3 × 3).
Can I save the results?
Yes, click the Save to History button to store the calculation in your local browser history.
Does it work on mobile?
Yes, the calculator is fully responsive and the keypad makes it easy to type on mobile.
What is the largest exponent I can enter?
There is no hard limit, but results exceeding 1e308 will return Infinity.
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