Math
Multiplying Exponents Calculator
Multiply two powers and see exactly which exponent rule applies.
Same base: a^m × a^n = a^(m+n), so 2^3 × 2^4 = 2^7. Same exponent: a^n × b^n = (ab)^n. Use a letter as the base for symbolic answers or a number for an exact evaluated result.
A number (2, -3, 1/2) or a letter (x).
Try an example
Result
Simplified
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- Original expression
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- Value
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- Rule
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Two rules for multiplying powers
| Situation | Rule | Example |
|---|---|---|
| Same base | a^m × a^n = a^(m+n) | x^3 × x^4 = x^7 |
| Same exponent | a^n × b^n = (ab)^n | 2^4 × 3^4 = 6^4 = 1,296 |
| Neither | no shortcut; evaluate each | 2^3 × 3^2 = 8 × 9 = 72 |
Why the exponents add
An The small raised number saying how many times to multiply the base by itself. counts repeated factors. 2^3 × 2^4 = (2 × 2 × 2) × (2 × 2 × 2 × 2) = 2^7. Counting the factors is the same as adding the exponents. The rule holds for negative and fractional exponents too, because those are defined so that the counting logic keeps working.
Negative and fractional exponents
- x^5 × x^-2 = x^3: adding a negative exponent subtracts factors.
- x^(1/2) × x^(1/2) = x^1 = x: two square roots multiply to the number itself.
- 2^-3 × 2^-1 = 2^-4 = 1/16.
How to use it
- Choose same The number being raised to a power, or the side a shape's height is measured from. if both powers share a base, or same exponent if they share an exponent.
- Enter the base(s) as numbers or a single letter and the exponent(s).
- Read the simplified power, its evaluated value when the bases are numeric, and the rule used.
How to read the answer
With the same base, the exponents add because you are stacking groups of the same factor: 2^3 × 2^4 is three 2s times four 2s, seven 2s in all. With the same exponent, the bases multiply inside the power because each pair of factors can be regrouped.
Common mistakes and edge cases
- Multiplying the exponents instead of adding: 2^3 × 2^4 is 2^7, not 2^12.
- Multiplying the bases when they are the same: 2^3 × 2^4 is not 4^7.
- Adding exponents when bases differ and exponents differ: 2^3 × 3^2 has no shortcut; just evaluate to 72.
- Forgetting a negative exponent still adds: x^5 × x^-2 = x^3.
Worked examples
Same base, numeric
2^3 × 2^4 = 2^7 = 128
Simplified
2^7
Same base, variable
x^5 × x^-2 = x^3
Simplified
x^3
Same exponent
2^4 × 3^4 = 6^4 = 1,296
Simplified
6^4
Negative base
(-3)^2 × (-3)^3 = (-3)^5 = -243
Simplified
(-3)^5
Fractional exponents
x^(1/2) × x^(1/2) = x
Simplified
x
Exponents cancel to zero
5^3 × 5^-3 = 5^0 = 1
Simplified
5^0
Undefined
0^2 × 0^-5 = 0^-3 divides by zero
Simplified
Error
Frequently asked questions
What is the rule for multiplying exponents with the same base?+
Keep the base and add the exponents: a^m × a^n = a^(m+n). For example, x^3 × x^4 = x^7.
How do you multiply exponents with different bases?+
If the exponents are the same, multiply the bases: 2^4 × 3^4 = 6^4. If both base and exponent differ, there is no shortcut; evaluate each power and multiply.
Do you add or multiply exponents when multiplying?+
Add. Multiplying exponents is the rule for a power of a power, (a^m)^n = a^(mn), not for multiplying two powers.
What is x^2 times x^3?+
x^5. Same base, so add 2 + 3.
How do you multiply negative exponents?+
The same way: add them. 2^-3 × 2^-1 = 2^-4 = 1/16.
What happens when the exponents add to zero?+
Any nonzero base to the power 0 equals 1: 5^3 × 5^-3 = 5^0 = 1.
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