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