Question

question
fully simplify.
$(5xy^2)^2$
answer attempt 1 out of 2
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Explanation:

Step1: Apply power of a product rule

The power of a product rule states that \((ab)^n = a^n b^n\). So for \((5xy^2)^2\), we apply this rule to each factor inside the parentheses.
\((5xy^2)^2 = 5^2 \cdot x^2 \cdot (y^2)^2\)

Step2: Simplify each term

• Simplify \(5^2\): \(5^2 = 25\)
• For \((y^2)^2\), we use the power of a power rule \((a^m)^n = a^{m \cdot n}\), so \((y^2)^2 = y^{2 \cdot 2}=y^4\)
• The term \(x^2\) remains as it is.

Combining these results, we get \(25x^2y^4\)

Answer:

\(25x^2y^4\)