Question

question
fully simplify.
\\((3x^5y)^4\\)
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 \((3x^{5}y)^{4}\), we can apply this rule to each factor inside the parentheses: \(3^4 \cdot (x^{5})^4 \cdot y^4\).

Step2: Simplify each term

• Simplify \(3^4\): \(3^4 = 3\times3\times3\times3 = 81\).
• Simplify \((x^{5})^4\) using the power of a power rule \((a^m)^n = a^{m\times n}\). So, \((x^{5})^4 = x^{5\times4} = x^{20}\).
• \(y^4\) remains as it is.

Now, multiply these simplified terms together: \(81 \cdot x^{20} \cdot y^4 = 81x^{20}y^4\).

Answer:

\(81x^{20}y^4\)