Example

Simplifying (3mn)3(-3mn)^3 and (2wx)5(2wx)^5 Using the Product to a Power Property

Apply the Product to a Power Property to simplify expressions where a product is raised to a power.

(3mn)3=27m3n3(-3mn)^3 = -27m^3n^3: The base is the product 3mn-3mn, which consists of three factors: 3-3, mm, and nn. Distribute the exponent 33 to each factor using (ab)m=ambm(ab)^m = a^m b^m: (3)3m3n3(-3)^3 \cdot m^3 \cdot n^3. Simplify the numerical part to get 27m3n3-27m^3n^3.

(2wx)5=32w5x5(2wx)^5 = 32w^5x^5: The base is 2wx2wx. Distribute the exponent 55 to the coefficient and the variables: 25w5x52^5 \cdot w^5 \cdot x^5. Evaluate 25=322^5 = 32 to obtain the simplified result 32w5x532w^5x^5.

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Updated 2026-04-29

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Ch.5 Polynomials and Polynomial Functions - Intermediate Algebra @ OpenStax

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