(3ab)^3 X (-2ab^4)/6ab^2

Jasonbradley

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Jun 16, 2024

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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

1. Simplify the cube:

   • (3ab)^3 = (3ab) * (3ab) * (3ab) = 27a^3b^3

2. Multiply the terms:

   • 27a^3b^3 * (-2ab^4) = -54a^4b^7

3. 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.