%5E3-x-(-2ab%5E4)%2F6ab%5E2.jpeg "(3ab)^3 X (-2ab^4)/6ab^2")
Simplifying Algebraic Expressions: (3ab)^3 x (-2ab^4)/6ab^2
This article will guide you through simplifying the algebraic expression: (3ab)^3 x (-2ab^4)/6ab^2.
Understanding the Expression
The expression involves:
- Exponents: We have terms raised to powers (3ab)^3 and ab^4.
- Multiplication and Division: The terms are connected by multiplication and division.
- Variables: The expression contains variables 'a' and 'b'.
Step-by-Step Simplification
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Simplify the cube:
- (3ab)^3 = (3ab) * (3ab) * (3ab) = 27a^3b^3
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Multiply the terms:
- 27a^3b^3 * (-2ab^4) = -54a^4b^7
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Divide by 6ab^2:
- -54a^4b^7 / 6ab^2 = -9a^3b^5
Final Simplified Expression
Therefore, the simplified form of the expression (3ab)^3 x (-2ab^4)/6ab^2 is -9a^3b^5.
Key Points to Remember
- Exponent Rule: (x^m)^n = x^(m*n)
- Multiplication Rule: x^m * x^n = x^(m+n)
- Division Rule: x^m / x^n = x^(m-n)
By understanding these basic rules and applying them systematically, you can simplify complex algebraic expressions like the one presented above.