Question

question
fully simplify.
$(-2xy^3)^2$

Explanation:

Step1: Apply power of a product rule

The power of a product rule states that \((ab)^n = a^n b^n\). So we can apply this to \((-2xy^{3})^{2}\) as follows:
\((-2xy^{3})^{2}=(-2)^{2}\cdot x^{2}\cdot (y^{3})^{2}\)

Step2: Simplify each term

• Simplify \((-2)^{2}\): \((-2)^{2}=(-2)\times(-2) = 4\)
• Simplify \(x^{2}\): It remains as \(x^{2}\) since the exponent of \(x\) is 1 and when we raise it to the power of 2, we use the power - of - a - power rule \((a^{m})^{n}=a^{mn}\), so \(x^{1\times2}=x^{2}\)
• Simplify \((y^{3})^{2}\): Using the power - of - a - power rule \((a^{m})^{n}=a^{mn}\), we have \(y^{3\times2}=y^{6}\)

Step3: Multiply the simplified terms together

Multiply the results from step 2: \(4\times x^{2}\times y^{6} = 4x^{2}y^{6}\)

Answer:

\(4x^{2}y^{6}\)