(3ab%5E4)%5E3.jpeg "(2a^3b^2)(3ab^4)^3")
Simplifying Algebraic Expressions: (2a^3b^2)(3ab^4)^3
This article will guide you through simplifying the algebraic expression (2a^3b^2)(3ab^4)^3.
Understanding the Order of Operations
To solve this, we need to follow the order of operations, commonly remembered by the acronym PEMDAS or BODMAS:
- Parentheses/ Brackets
- Exponents/ Orders
- Multiplication and Division (from left to right)
- Addition and Subtraction (from left to right)
Step-by-Step Solution
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Simplify the exponent:
- (3ab^4)^3 = (3^3)(a^3)(b^4)^3 = 27a^3b^12
- Remember that when raising a power to another power, you multiply the exponents.
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Multiply the results:
- (2a^3b^2)(27a^3b^12) = (2 * 27)(a^3 * a^3)(b^2 * b^12) = 54a^6b^14
- When multiplying variables with the same base, add the exponents.
Final Answer
The simplified form of the expression (2a^3b^2)(3ab^4)^3 is 54a^6b^14.
Conclusion
Simplifying algebraic expressions is crucial for various mathematical operations and problem-solving. By understanding the order of operations and applying the correct rules for exponents and multiplication, you can efficiently simplify complex expressions like the one presented here.