Question

score: 0/3 penalty: 1 off
question
fully simplify.
$(-3x^3y^4)^4$
answer attempt 2 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 \((-3x^{3}y^{4})^{4}\), we can apply this rule to each factor inside the parentheses: \((-3)^{4}(x^{3})^{4}(y^{4})^{4}\).

Step2: Simplify each factor

• Simplify \((-3)^{4}\): \((-3)^{4}=(-3)\times(-3)\times(-3)\times(-3) = 81\).
• Simplify \((x^{3})^{4}\) using the power of a power rule \((a^m)^n=a^{mn}\): \((x^{3})^{4}=x^{3\times4}=x^{12}\).
• Simplify \((y^{4})^{4}\) using the power of a power rule: \((y^{4})^{4}=y^{4\times4}=y^{16}\).

Step3: Combine the simplified factors

Multiply the simplified factors together: \(81\times x^{12}\times y^{16}=81x^{12}y^{16}\).

Answer:

\(81x^{12}y^{16}\)