Question

$(-3x^{3}y^{3})^{4}$

Explanation:

Step1: Apply power of a product rule

The power of a product rule states that \((ab)^n = a^n b^n\). So we can apply this to \((-3x^{3}y^{3})^{4}\) as follows:
\((-3x^{3}y^{3})^{4}=(-3)^{4}\cdot(x^{3})^{4}\cdot(y^{3})^{4}\)

Step2: Calculate each term

• Calculate \((-3)^{4}\): \((-3)^{4}=(-3)\times(-3)\times(-3)\times(-3) = 81\)
• Calculate \((x^{3})^{4}\) using the power of a power rule \((a^m)^n=a^{mn}\): \((x^{3})^{4}=x^{3\times4}=x^{12}\)
• Calculate \((y^{3})^{4}\) using the power of a power rule: \((y^{3})^{4}=y^{3\times4}=y^{12}\)

Step3: Multiply the results together

Multiply the three results we got: \(81\times x^{12}\times y^{12}=81x^{12}y^{12}\)

Answer:

\(81x^{12}y^{12}\)