(4ab%5E2)%5E2.jpeg "(3a^3b^3)(4ab^2)^2")
Simplifying the Expression (3a³b³)(4ab²)²
This article will guide you through simplifying the expression (3a³b³)(4ab²)². We'll use the rules of exponents and order of operations to achieve a simplified form.
Understanding the Expression
The expression involves:
- Coefficients: Numbers like 3 and 4
- Variables: Letters representing unknown values (a and b)
- Exponents: Numbers indicating how many times a base is multiplied by itself (e.g., a³ = a * a * a)
- Parentheses: Indicating the order of operations
Simplifying Steps
-
Simplify the exponent:
- (4ab²)² means (4ab²) * (4ab²).
- Apply the distributive property: 4 * 4 * a * a * b² * b² = 16a²b⁴
-
Multiply the terms inside and outside the parentheses:
- (3a³b³) * (16a²b⁴) = 48a⁵b⁷
Final Result
The simplified form of the expression (3a³b³)(4ab²)² is 48a⁵b⁷.
Key Takeaways
- Exponent rule: When raising a product to a power, apply the exponent to each factor within the product.
- Order of operations: Simplify exponents before multiplication.
- Combining like terms: Multiply coefficients and combine variables with the same base by adding their exponents.
By following these rules and steps, you can efficiently simplify expressions involving exponents and variables.