Question

(3xyz·xy²z)³

Explanation:

Step1: Simplify inside the parentheses

First, multiply the terms inside the parentheses. When multiplying variables with exponents, we add the exponents for like bases. For the coefficient, we have 3. For \(x\): \(x \cdot x = x^{1 + 1}=x^{2}\). For \(y\): \(y \cdot y^{2}=y^{1 + 2}=y^{3}\). For \(z\): \(z \cdot z = z^{1 + 1}=z^{2}\). So inside the parentheses, we get \(3x^{2}y^{3}z^{2}\).

Step2: Apply the exponent to the entire term

Now, we raise the entire term \(3x^{2}y^{3}z^{2}\) to the power of 3. We raise each factor to the power of 3. For the coefficient: \(3^{3}=27\). For \(x\): \((x^{2})^{3}=x^{2\times3}=x^{6}\). For \(y\): \((y^{3})^{3}=y^{3\times3}=y^{9}\). For \(z\): \((z^{2})^{3}=z^{2\times3}=z^{6}\). Then we multiply all these together: \(27x^{6}y^{9}z^{6}\).

Answer:

\(27x^{6}y^{9}z^{6}\)