Questions: Raising a Product or a Quotient to a Power Simplify each of the following. 27. (-6xy^2)^2

Solution Steps

The expression given is \(\left(-6 x y^{2}\right)^{2}\). According to the power of a product rule, \((ab)^n = a^n b^n\), we apply the exponent to each factor inside the parentheses:

\[ \left(-6 x y^{2}\right)^{2} = (-6)^{2} \cdot (x)^{2} \cdot (y^{2})^{2} \]

Now, simplify each term separately:

1. \((-6)^{2} = 36\)
2. \((x)^{2} = x^{2}\)
3. \((y^{2})^{2} = y^{4}\)

Combine the simplified terms to get the final expression:

\[ 36 \cdot x^{2} \cdot y^{4} = 36x^{2}y^{4} \]

Final Answer