%5E2.jpeg "(5xy^3)^2")
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.