# Explanation: ## Step1: Apply power of a product rule The power of a product rule states that $(ab)^n = a^n b^n$. So for $(-5xy^2)^2$, we can apply this rule to each factor: $(-5)^2 \cdot x^2 \cdot (y^2)^2$. ## Step2: Simplify each factor - Simplify $(-5)^2$: $(-5)^2 = 25$. - Simplify $(y^2)^2$ using the power of a power rule $(a^m)^n = a^{mn}$, so $(y^2)^2 = y^{2\times2} = y^4$. - The $x$ term remains $x^2$ as is. Now multiply the simplified factors together: $25 \cdot x^2 \cdot y^4 = 25x^2y^4$. # Answer: $25x^2y^4$

$(-5xy^{2})^{2}$

QUESTION IMAGE

$(-5xy^{2})^{2}$

Question

$(-5xy^{2})^{2}$

Explanation:

Step1: Apply power of a product rule

The power of a product rule states that $(ab)^n = a^n b^n$. So for $(-5xy^2)^2$, we can apply this rule to each factor: $(-5)^2 \cdot x^2 \cdot (y^2)^2$.

Step2: Simplify each factor

Simplify $(-5)^2$: $(-5)^2 = 25$.
Simplify $(y^2)^2$ using the power of a power rule $(a^m)^n = a^{mn}$, so $(y^2)^2 = y^{2\times2} = y^4$.
The $x$ term remains $x^2$ as is.

Now multiply the simplified factors together: $25 \cdot x^2 \cdot y^4 = 25x^2y^4$.

Answer:

$25x^2y^4$