Question

question
fully simplify.
\\((6xy^2)^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 \((6xy^2)^5\), we can apply this rule to each factor inside the parentheses:
\((6xy^2)^5 = 6^5 \cdot x^5 \cdot (y^2)^5\)

Step2: Simplify each term

• Calculate \(6^5\): \(6^5 = 6\times6\times6\times6\times6 = 7776\)
• For \((y^2)^5\), we use the power of a power rule \((a^m)^n = a^{m\times n}\), so \((y^2)^5 = y^{2\times5} = y^{10}\)

Putting it all together, we have:
\(6^5 \cdot x^5 \cdot (y^2)^5 = 7776x^5y^{10}\)

Answer:

\(7776x^5y^{10}\)