Question

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fully simplify.
(3xy²)⁵
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 \((3xy^2)^5\), we can apply this rule to each factor inside the parentheses: \(3^5 \cdot x^5 \cdot (y^2)^5\).

Step2: Simplify each term

• Calculate \(3^5\): \(3^5 = 3\times3\times3\times3\times3 = 243\).
• For \((y^2)^5\), use the power of a power rule \((a^m)^n = a^{mn}\). So, \((y^2)^5 = y^{2\times5} = y^{10}\).
• The \(x^5\) term remains as is.

Combining these results, we get \(243x^5y^{10}\).

Answer:

\(243x^5y^{10}\)