Question

question
fully simplify.
\\((3x^5y)^5\\)

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 \((3x^{5}y)^{5}\) as follows:
\((3x^{5}y)^{5}=3^{5}\times(x^{5})^{5}\times y^{5}\)

Step2: Calculate each term

• Calculate \(3^{5}\): \(3^{5}=3\times3\times3\times3\times3 = 243\)
• Calculate \((x^{5})^{5}\) using the power of a power rule \((a^{m})^{n}=a^{mn}\): \((x^{5})^{5}=x^{5\times5}=x^{25}\)
• \(y^{5}\) remains as it is.

Step3: Combine the terms

Multiply the results together: \(243\times x^{25}\times y^{5}=243x^{25}y^{5}\)

Answer:

\(243x^{25}y^{5}\)