new Maths

Powers and Roots Calculator

Calculate a base raised to an exponent, find a real nth root, and evaluate a natural logarithm in one place.

Powers, roots, and logarithms
Power
Nth root
Power result
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base raised to exponent
Nth root
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Natural logarithm
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✓ Powers and roots ✓ Natural logarithms ✓ Shows working ✓ Browser-based

How to use powers and roots

Enter values for each operation and read the three live results.

1

Enter the power

Type a base and exponent to calculate the base raised to that exponent.

2

Enter the root

Provide a value and a whole-number root degree, such as 27 and 3 for the cube root.

3

Enter the logarithm value

Use a positive value for ln; the calculator displays the natural logarithm and its working.

Frequently Asked Questions

What does a power calculate?

A power multiplies a base by itself the specified number of times; for example, 2⁸ is 256.

How is an nth root calculated?

The nth root of x is equivalent to <strong>x^(1/n)</strong> for real results.

What is the difference between a square root and a cube root?

A square root uses degree 2, while a cube root uses degree 3. The degree tells you which power returns the original value.

What is a natural logarithm?

The natural logarithm ln(x) is the logarithm with base e, approximately 2.71828.

Can I find the root of a negative number?

Odd roots of negative values can be real, but even roots of negative values are not real and will be rejected.

Why must ln values be positive?

The real-valued natural logarithm is defined only for values greater than zero.

Does the calculator support decimal exponents?

Yes. The power operation accepts finite decimal bases and exponents, subject to the limits of real-number arithmetic.