Question

question
fully simplify.
$(-3xy^3)^2$
answer attempt 1 out of 5

Explanation:

Step1: Apply power of a product rule

The power of a product rule states that \((ab)^n = a^n b^n\). So for \((-3xy^3)^2\), we can apply this rule to each factor: \((-3)^2 \cdot x^2 \cdot (y^3)^2\).

Step2: Simplify each factor

• Simplify \((-3)^2\): \((-3)^2 = 9\).
• For \((y^3)^2\), use the power of a power rule \((a^m)^n = a^{mn}\), so \((y^3)^2 = y^{3 \times 2} = y^6\).
• The \(x\) term becomes \(x^2\) as per the power of a product rule.

Step3: Combine the simplified factors

Multiply the simplified factors together: \(9 \cdot x^2 \cdot y^6 = 9x^2y^6\).

Answer:

\(9x^2y^6\)