Question

simplify.
\\((-4y^{2}x^{4})^{3}\\)
write your answer without parent

Explanation:

Step1: Apply the 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 \((-4y^{2}x^{4})^{3}\) as follows:
\((-4y^{2}x^{4})^{3}=(-4)^{3}(y^{2})^{3}(x^{4})^{3}\)

Step2: Calculate each part

• Calculate \((-4)^{3}\): \((-4)^{3}=(-4)\times(-4)\times(-4)= -64\)
• Calculate \((y^{2})^{3}\) using the power of a power rule \((a^m)^n = a^{mn}\): \((y^{2})^{3}=y^{2\times3}=y^{6}\)
• Calculate \((x^{4})^{3}\) using the power of a power rule: \((x^{4})^{3}=x^{4\times3}=x^{12}\)

Step3: Multiply the results together

Multiply the three results we got: \(-64\times y^{6}\times x^{12}=-64x^{12}y^{6}\)

Answer:

\(-64x^{12}y^{6}\)