What is the power of a power rule?

The power of a power rule states that when raising a power to another exponent, you multiply the exponents: (a^m)^n = a^(m*n). For example, (2^3)^2 = 2^(3*2) = 2^6 = 64.

How do I use this calculator?

Enter a base number, the first exponent, and the second exponent. The calculator will apply the rule by multiplying the two exponents and show the simplified result as a^ (first exponent × second exponent).

Can I use negative exponents?

Yes, you can enter negative exponents. The rule still applies: multiply the exponents. For example, (2^-2)^3 = 2^(-6) = 1/64. The calculator will handle the multiplication and display the result.

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Power of a Power Calculator.

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Use Cases

Simplify algebraic expressions

Quickly simplify nested exponents in algebra homework or when working with exponential functions, saving time and reducing errors.

Example: Simplify (x^3)^4 to x^12.

Check manual calculations

Verify your own application of the power-of-a-power rule when solving math problems or preparing for exams.

Example: Check that (5^2)^3 equals 5^6 = 15625.

Frequently Asked Questions

What is the power of a power rule?: The power of a power rule states that when raising a power to another exponent, you multiply the exponents: (a^m)^n = a^(m*n). For example, (2^3)^2 = 2^(3*2) = 2^6 = 64.
How do I use this calculator?: Enter a base number, the first exponent, and the second exponent. The calculator will apply the rule by multiplying the two exponents and show the simplified result as a^ (first exponent × second exponent).
Can I use negative exponents?: Yes, you can enter negative exponents. The rule still applies: multiply the exponents. For example, (2^-2)^3 = 2^(-6) = 1/64. The calculator will handle the multiplication and display the result.

Tips & Common Mistakes

Tips

Remember to multiply the exponents, not add them. For (a^m)^n, the result is a^(m*n).
If the base is negative, the sign depends on the final exponent. For example, (-2)^3 = -8, but (-2)^4 = 16.
When exponents are fractions, the rule still works: (a^(1/2))^2 = a^(1) = a.
Use the calculator to practice with different numbers and build confidence in applying the rule.

Common Mistakes to Avoid

Adding the exponents instead of multiplying them. For (2^3)^2, some mistakenly write 2^5 instead of 2^6.
Forgetting to apply the rule to the base if it has a coefficient. For example, (2x^3)^2 should be 4x^6, not 2x^6.
Confusing the power of a power rule with the product of powers rule (a^m * a^n = a^(m+n)).

Last updated: August 13, 2026