Evaluate a^n for integer and real exponents, or take an n-th root, with the product and reciprocal steps used on paper.
2^5 = 32
- 2 × 2 × 2 × 2 × 2 = 32.
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How to Use the Exponent Calculator
Choose Power or n-th root, enter the two numbers, and select Evaluate. Integer powers show the repeated product. Negative powers show the reciprocal. Roots show a^(1/n) and a check by raising the answer back.
- Select Power a^n or n-th root.
- Enter a finite base and exponent, or an integer index and a radicand.
- Read the value, the scientific form, and the reciprocal.
Writing a number as a × 10^n belongs on the Scientific Notation Calculator. Recovering the exponent from b^x = a belongs on the Logarithm Calculator. x² in an equation belongs on the Quadratic Formula Calculator. This page only evaluates one power or one real root.
Integer, Negative, and Fractional Exponents
A whole-number exponent counts how many times the base is a factor. 2^5 has five factors of 2. The exponent 0 on a nonzero base is the empty product, which is 1.
A negative exponent does not make the answer negative. It writes a reciprocal: 2^(−3) = 1 / 2^3 = 1/8. A fractional exponent 1/n is the n-th root. This page stays in the real numbers, so even roots of negatives and 0^0 are rejected.
Exponent Calculator Examples
A positive integer power
2^5 = 2 × 2 × 2 × 2 × 2 = 32.
A zero exponent
5^0 = 1. Any nonzero base to the power 0 is 1.
A negative exponent
2^(−3) = 1 / 8 = 0.125.
A negative base and even power
(−2)^4 = 16. An even number of negative factors is positive.
A square root
The 2nd root of 9 is 3, because 3^2 = 9.
Roots
Switch to n-th root to enter the index and the radicand instead of typing 1/n as an exponent. The cube root of 8 is 2. An even root of a negative number is not real on this page. An odd root keeps the sign: the cube root of −8 is −2.
Common Exponent Mistakes
Reading 2^5 as 2 × 5
2^5 is five factors of 2, which is 32, not 10.
Making a negative exponent a negative answer
2^(−3) is 1/8, which is positive. The minus sits on the exponent, not on the value, unless the base is negative and the exponent is odd.
Writing 0^0
That form is undefined in this classroom setting. The calculator rejects it.
Taking an even root of a negative
√(−9) is not real. Change the sign or use an odd index.
Confusing this with scientific notation
4.5 × 10^4 is a place-value rewrite. Evaluate 10^4 = 10000 here, then use the Scientific Notation Calculator to move the point.
Exponent Calculator FAQs
How do you calculate 2^5?
Multiply five factors of 2: 2 × 2 × 2 × 2 × 2 = 32.
What is 2 to the power −3?
1 / 2^3 = 1/8 = 0.125.
Why is any nonzero number to the power 0 equal to 1?
It is the empty product, and it keeps the law a^m / a^m = a^0 = 1.
Can I take a root?
Yes. Use n-th root mode, or enter the exponent 0.5 for a square root of a nonnegative base.
Does this write a number in scientific notation?
It shows a scientific form of the value. To convert 45000 to 4.5 × 10^4 with place-value steps, use the Scientific Notation Calculator.
Are my numbers sent to a server?
No. The calculation runs locally in your browser.
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Reviewed by Prof. Dr. Khalil Mudassar (PhD) · Last updated: [mc_modified_date]
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Disclaimer
This calculator is for general educational use. It evaluates real powers and real n-th roots. It does not simplify variable expressions or work in the complex numbers.