(-4a^2b)(-3a^7b)/6a^7b^2

Jasonbradley

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Jun 16, 2024

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Simplifying Algebraic Expressions: (-4a^2b)(-3a^7b)/6a^7b^2

This article will guide you through the process of simplifying the algebraic expression (-4a^2b)(-3a^7b)/6a^7b^2.

Understanding the Expression

The expression involves multiplication and division of terms with variables and exponents. Let's break it down:

• Numerator: We have (-4a^2b)(-3a^7b) which represents the product of two binomials.
• Denominator: We have 6a^7b^2 which is a single term.

Simplifying the Expression

1. Multiplication in the Numerator:

   • Multiply the coefficients: (-4) * (-3) = 12
   • Multiply the variables: a^2 * a^7 = a^(2+7) = a^9, and b * b = b^2.
   • The numerator becomes 12a^9b^2.

2. Combining Numerator and Denominator:

   • We have (12a^9b^2) / (6a^7b^2)

3. Dividing Variables with Exponents:

   • Divide the coefficients: 12 / 6 = 2
   • Divide the variables with exponents: a^9 / a^7 = a^(9-7) = a^2, and b^2 / b^2 = b^(2-2) = b^0 = 1.

4. Final Result:

   • The simplified expression is 2a^2.

Conclusion

By applying the rules of multiplication and division of exponents, we have successfully simplified the expression (-4a^2b)(-3a^7b)/6a^7b^2 to 2a^2. Remember, when dividing variables with exponents, we subtract the powers of the same base.