Multiplying Exponents Calculator
Simplify expressions with exponents: choose the product rule (same base, add exponents) or the power-of-a-power rule (multiply exponents), then get the simplified form and numeric value.
Rule
Write out the product
Add the exponents (same base)
Simplified form
Numeric value
- 1
Add the exponents (product rule)
3 + 4 = 7When two powers share the same base, their exponents add. - 2
Evaluate 2^7
2^7 = 128
How does this calculator work?
Product rule: xᵐ · xⁿ = x^(m+n) — same base, add the exponents. Power rule: (xᵐ)ⁿ = x^(m·n) — power of a power, multiply the exponents. Both follow from counting how many times the base appears as a factor. Enter the base and two exponents, pick the rule, and get the simplified form and its numeric value.
Formula
How this is calculated
When two powers with the same base are multiplied, the exponents add: xᵐ · xⁿ = x^(m+n). This is the product rule. The intuition is direct — xᵐ is m copies of x, xⁿ is n copies, so their product is m+n copies of x altogether. The rule applies to any real base and any real exponents, including negatives (x³ · x⁻¹ = x²) and fractions (x^½ · x^½ = x¹ = x).
When a power is itself raised to another exponent, the two exponents multiply: (xᵐ)ⁿ = x^(m·n). This is the power rule. Here (xᵐ)ⁿ means n copies of xᵐ, and each contributes m factors of x, giving m·n total factors. For example, (x²)³ = x^(2·3) = x⁶.
Both rules extend naturally to negative and fractional exponents. For very large combined exponents the numeric value overflows the floating-point range (greater than about 10^308 for base > 1) and is shown as "Overflow" — the simplified symbolic form x^k is still correct. Powers of negative bases with non-integer exponents may produce complex results not shown here.
Frequently asked questions
The product rule applies when two separate powers share a base: xᵐ · xⁿ = x^(m+n) — add the exponents. The power rule applies when a power is raised to another exponent: (xᵐ)ⁿ = x^(m·n) — multiply the exponents. They describe different operations even though both involve combining exponents.
Yes. For the product rule: x³ · x⁻² = x^(3−2) = x¹. For the power rule: (x^(1/2))² = x^(1/2·2) = x. Negative exponents denote reciprocals (x^(−n) = 1/xⁿ) and fractional exponents denote roots (x^(1/n) is the n-th root of x).
Not directly with these two rules. The product rule requires the same base. However, if the exponents are equal, xⁿ · yⁿ = (xy)ⁿ. For completely different bases and exponents (e.g. 2³ · 5²) there is no algebraic simplification — evaluate each power separately and multiply the results.
Also known as
TG we-Calculate Editorial Team. (2026). Multiplying Exponents Calculator [Online calculator]. TG we-Calculate. https://we-calculate.com/calculator/multiplying-exponents-calculator
TG we-Calculate Editorial Team. "Multiplying Exponents Calculator." TG we-Calculate. 2026. https://we-calculate.com/calculator/multiplying-exponents-calculator.
TG we-Calculate Editorial Team, "Multiplying Exponents Calculator," TG we-Calculate, 2026. [Online]. Available: https://we-calculate.com/calculator/multiplying-exponents-calculator
@misc{wecalculate_multiplying_exponents_calculator, title = {Multiplying Exponents Calculator}, author = {{TG we-Calculate Editorial Team}}, howpublished = {\url{https://we-calculate.com/calculator/multiplying-exponents-calculator}}, year = {2026}, note = {TG we-Calculate} }
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