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.

数学

即时、私密且免费

Power of a Power Calculator.

Apply (aᵐ)ⁿ = aᵐⁿ.

设备端计算无需注册

输入数值

输入时结果会更新。

02 / 答案

Base

First exponent

Second exponent

Combined exponent

数值

Results update automatically as you type.

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