Simplify (3x^2 y)^3

Answer

\boxed{27x^6 y^3}

Checking by expanding the product gives $(3x^2y)(3x^2y)(3x^2y) = (3 \cdot 3 \cdot 3)(x^2 \cdot x^2 \cdot x^2)(y \cdot y \cdot y) = 27x^6y^3$ , which confirms the result.

Problem: Simplify the expression $(3x^2 y)^3$ .

Steps

Apply the power of a product rule $3^3 (x^2)^3 y^3$
Evaluate the numerical power $27 (x^2)^3 y^3$
Apply the power of a power rule $27 x^{2 \cdot 3} y^3$
Simplify the exponent $27 x^6 y^3$

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