## Simplifying the Expression (5xy^3)^2

This article will explore the simplification of the algebraic expression (5xy^3)^2.

### Understanding the Concept

The expression (5xy^3)^2 represents the square of the entire term within the parentheses. This means we multiply the term by itself.

### Applying the Exponent Rule

We can use the rule of exponents that states: (a*b)^n = a^n * b^n. This rule allows us to distribute the exponent to each factor within the parentheses.

Applying this to our expression, we get:

(5xy^3)^2 = 5^2 * x^2 * (y^3)^2

### Simplifying Further

Now, we simplify the individual exponents:

5^2 = 25 x^2 = x^2 (y^3)^2 = y^(3*2) = y^6

### Final Solution

Combining these simplified terms, the final answer is:

**(5xy^3)^2 = 25x^2y^6**

### Conclusion

By applying the appropriate exponent rules, we can simplify complex expressions like (5xy^3)^2 into a more concise and understandable form. This simplification allows for easier manipulation and understanding of algebraic equations.