%5E2(3a%5E2b).jpeg "(-4a^3b^2)^2(3a^2b)")
Simplifying the Expression (-4a^3b^2)^2(3a^2b)
This article will guide you through simplifying the expression (-4a^3b^2)^2(3a^2b).
Understanding the Order of Operations
Before we begin simplifying, let's recall the order of operations, often remembered by the acronym PEMDAS or BODMAS:
- Parentheses (or Brackets)
- Exponents (or Orders)
- Multiplication and Division (from left to right)
- Addition and Subtraction (from left to right)
Simplifying the Expression
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Simplify the exponent:
- (-4a^3b^2)^2 = (-4)^2 (a^3)^2 (b^2)^2 = 16a^6b^4
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Multiply the simplified terms:
- 16a^6b^4 * 3a^2b = 48a^8b^5
Final Result
Therefore, the simplified form of the expression (-4a^3b^2)^2(3a^2b) is 48a^8b^5.
Key Concepts Used
- Exponent Rule: (x^m)^n = x^(m*n)
- Multiplication of Variables with Exponents: x^m * x^n = x^(m+n)