(-3a%5E7b)%2F6a%5E7b%5E2%2B16a%5E2.jpeg "(-4a^2b)(-3a^7b)/6a^7b^2+16a^2")
Simplifying Algebraic Expressions: (-4a^2b)(-3a^7b)/6a^7b^2+16a^2
This article will guide you through simplifying the algebraic expression (-4a^2b)(-3a^7b)/6a^7b^2+16a^2. We'll break down the steps involved and explain the key concepts used.
Step 1: Simplify the Numerator
- Multiplication of Monomials: Multiply the coefficients and add the exponents of like bases.
- (-4a^2b)(-3a^7b) = 12a^(2+7)b^(1+1) = 12a^9b^2
Step 2: Simplify the Denominator
- No simplification needed: The denominator is already in its simplest form, as there are no common factors that can be cancelled out.
Step 3: Combine the Simplified Numerator and Denominator
- Dividing Monomials: Divide the coefficients and subtract the exponents of like bases.
- 12a^9b^2 / 6a^7b^2 = (12/6)a^(9-7)b^(2-2) = 2a^2
Step 4: Combine the Simplified Result with the Remaining Term
- Adding Terms: The remaining term is 16a^2. Since both terms now have the same base and exponent (a^2), we can add their coefficients.
- 2a^2 + 16a^2 = (2+16)a^2 = 18a^2
Final Result
Therefore, the simplified form of the expression (-4a^2b)(-3a^7b)/6a^7b^2+16a^2 is 18a^2.
Key Concepts:
- Monomials: An algebraic expression with a single term, containing a coefficient and variables raised to non-negative integer exponents.
- Coefficients: Numerical factors in an algebraic expression.
- Exponents: Indicate the number of times a base is multiplied by itself.
- Simplifying Expressions: Reducing an expression to its simplest form by applying algebraic rules.
Remember, simplifying expressions involves applying the rules of arithmetic and algebra. By breaking down the problem into smaller steps, you can confidently simplify even complex expressions.