Questions: (-3xy^3)^2

Solution Steps

To simplify the expression \(\left(-3 x y^{3}\right)^{2}\), we need to apply the power of a power rule. This rule states that when raising a power to another power, you multiply the exponents. We will apply this rule to each component inside the parentheses: the constant \(-3\), the variable \(x\), and the variable \(y^3\).

To simplify the expression \(\left(-3 x y^{3}\right)^{2}\), we apply the power of a power rule, which states that \((a^m)^n = a^{m \cdot n}\). This means we will raise each component inside the parentheses to the power of 2.

1. For the constant: \[ (-3)^{2} = 9 \]
2. For the variable \(x\): \[ (x^{1})^{2} = x^{2} \]
3. For the variable \(y^{3}\): \[ (y^{3})^{2} = y^{6} \]

Combining all the simplified components, we get: \[ 9 x^{2} y^{6} \]

Final Answer