Math
Power of a Power Calculator
Raise a power to another power and see the rule (a^m)^n = a^(m×n) applied: (2^3)^2 = 2^6 = 64.
Works with letters as the base for algebra homework, with negative exponents like (x^-2)^3, and with fractional exponents like (x^6)^(1/2).
A number (2, -3, 1/2) or a letter (x).
The exponent inside the parentheses.
The exponent outside the parentheses.
Try an example
Result
Simplified
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- Value
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- Original
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Student quick launch
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Study path
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The power of a power rule
(2^3)^2 means 2^3 × 2^3. Using the product rule that is 2^(3+3) = 2^6. Repeating a power n times adds m to itself n times, which is m × n. So the The small raised number saying how many times to multiply the base by itself. multiply.
Add or multiply? Compare the rules
| Expression | Rule | Result |
|---|---|---|
| x^2 · x^3 | product: add exponents | x^5 |
| (x^2)^3 | power of a power: multiply exponents | x^6 |
| x^6 ÷ x^2 | quotient: subtract exponents | x^4 |
| (xy)^3 | power of a product: apply to each factor | x^3 y^3 |
Fractional and negative outer exponents
- (x^6)^(1/2) = x^3: a square root halves the exponent.
- (x^-2)^3 = x^-6 = 1 / x^6.
- (x^-2)^-3 = x^6: two negatives multiply to a positive.
- (8^(1/3))^2 = 8^(2/3) = 4.
How to use it
- Enter the base as a number or a letter.
- Enter the inner exponent m and the outer exponent n.
- Read the simplified power a^(mn) and its value when the The number being raised to a power, or the side a shape's height is measured from. is numeric.
How to read the answer
The outer exponent tells you how many copies of the inner power to multiply. Each copy carries m factors of the base, so n copies carry m × n factors. That is why the exponents multiply here, while they add when you multiply two powers side by side.
Common mistakes and edge cases
- Adding instead of multiplying: (x^2)^3 = x^6, not x^5.
- Mixing this up with x^2 · x^3 = x^5, where the exponents add.
- Forgetting the sign: (x^-2)^3 = x^-6 = 1/x^6.
- Applying the outer exponent only to the base and not to a The number multiplying a variable, like the 3 in 3x.: (3x^2)^2 = 9x^4.
Worked examples
Numeric
(2^3)^2 = 2^6 = 64
Simplified
2^6
Variable
(x^2)^3 = x^6
Simplified
x^6
Negative inner exponent
(x^-2)^3 = x^-6
Simplified
x^(-6)
Square root outside
(x^6)^(1/2) = x^3
Simplified
x^3
Negative base
((-3)^2)^2 = (-3)^4 = 81
Simplified
(-3)^4
Exponents that cancel
(5^2)^0 = 5^0 = 1
Simplified
5^0
Undefined
(0^2)^-1 divides by zero
Simplified
Error
Frequently asked questions
What is the power of a power rule?+
(a^m)^n = a^(mn). Multiply the exponents and keep the base: (x^2)^3 = x^6.
Do you add or multiply exponents in (x^2)^3?+
Multiply: 2 × 3 = 6. Adding is for x^2 · x^3, which gives x^5.
What is (2^3)^2?+
2^6 = 64. Check: 2^3 = 8 and 8^2 = 64.
How does the rule work with negative exponents?+
Multiply with signs: (x^-2)^3 = x^-6 = 1/x^6, and (x^-2)^-3 = x^6.
What about a fraction as the outer exponent?+
It works the same way: (x^6)^(1/2) = x^3. A 1/2 power is a square root, which halves the exponent.
Does the rule apply to (3x^2)^2?+
Yes, but the 3 gets squared too: (3x^2)^2 = 3^2 · (x^2)^2 = 9x^4. Apply the outer exponent to every factor inside.
About this calculator
- Written by
- mathcheck editorial team
- Last reviewed
- September 4, 2026
Method
- Uses the values entered by the user and stable formulas documented on the page.
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Last updated: September 4, 2026