Simplifying (4y^3)^2
This expression involves a few key concepts in algebra: exponents, multiplication, and the order of operations. Let's break it down stepbystep.
Understanding the Components
 (4y^3): This is a monomial, meaning it's a single term with a coefficient (4) and a variable (y) raised to a power (3).
 ^2: This is an exponent, indicating that the entire monomial (4y^3) should be multiplied by itself.
Applying the Rules

Distributing the Exponent: When raising a product to a power, we distribute the exponent to each factor within the parentheses.
 (4y^3)^2 = (4)^2 * (y^3)^2

Simplifying the Exponents: When raising a power to another power, we multiply the exponents.
 (4)^2 * (y^3)^2 = 16 * y^(3*2) = 16y^6
The Final Answer
Therefore, (4y^3)^2 simplifies to 16y^6.
Key Points to Remember
 Order of operations (PEMDAS/BODMAS): Parentheses/Brackets first, then Exponents, Multiplication and Division (from left to right), finally Addition and Subtraction (from left to right).
 Exponent rules: When raising a product to a power, distribute the exponent to each factor. When raising a power to another power, multiply the exponents.