Question

fully simplify.
(3x³y⁵)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 \((3x^{3}y^{5})^{4}\) as follows:
\((3x^{3}y^{5})^{4}=3^{4}\cdot(x^{3})^{4}\cdot(y^{5})^{4}\)

Step2: Simplify each term

• For \(3^{4}\), we calculate \(3\times3\times3\times3 = 81\).
• For \((x^{3})^{4}\), we use the power of a power rule \((a^m)^n=a^{m\times n}\), so \((x^{3})^{4}=x^{3\times4}=x^{12}\).
• For \((y^{5})^{4}\), using the power of a power rule again, we get \((y^{5})^{4}=y^{5\times4}=y^{20}\).

Step3: Combine the simplified terms

Multiplying the simplified terms together, we have \(3^{4}\cdot(x^{3})^{4}\cdot(y^{5})^{4}=81x^{12}y^{20}\).

Answer:

\(81x^{12}y^{20}\)