Question

question
fully simplify.
$(-3x^4y)^4$
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 \((-3x^{4}y)^{4}\), we can apply this rule to each factor: \((-3)^4 \cdot (x^{4})^4 \cdot y^4\).

Step2: Calculate each power

• Calculate \((-3)^4\): \((-3)^4 = (-3) \times (-3) \times (-3) \times (-3) = 81\).
• Calculate \((x^{4})^4\) using the power of a power rule \((a^m)^n = a^{mn}\): \((x^{4})^4 = x^{4 \times 4} = x^{16}\).
• \(y^4\) remains as it is.

Step3: Multiply the results together

Multiply the three results: \(81 \cdot x^{16} \cdot y^4 = 81x^{16}y^4\).

Answer:

\(81x^{16}y^4\)