Question

question
fully simplify.
$(5x^2y^5)^2$
answer attempt 1 out of 5
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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 \((5x^{2}y^{5})^{2}\), we can apply this rule to each factor inside the parentheses: \(5^{2}(x^{2})^{2}(y^{5})^{2}\).

Step2: Simplify each term

• Simplify \(5^{2}\): \(5^{2}=25\).
• Simplify \((x^{2})^{2}\) using the power of a power rule \((a^{m})^{n}=a^{mn}\). Here, \(m = 2\) and \(n = 2\), so \((x^{2})^{2}=x^{2\times2}=x^{4}\).
• Simplify \((y^{5})^{2}\) using the power of a power rule. Here, \(m = 5\) and \(n = 2\), so \((y^{5})^{2}=y^{5\times2}=y^{10}\).

Step3: Combine the simplified terms

Multiply the simplified terms together: \(25\times x^{4}\times y^{10}=25x^{4}y^{10}\).

Answer:

\(25x^{4}y^{10}\)