Simplify each expression. See Example 1. (5x²y)(-3x³y⁴)

Verified step by step guidance

1. Identify the expression to simplify: \((5x^2y)(-3x^3y^4)\).
2. Apply the associative property of multiplication to group the coefficients and the variables separately: \((5 imes -3)(x^2 imes x^3)(y imes y^4)\).
3. Multiply the coefficients: \$5 imes -3 = -15$.
4. Use the product of powers property for the variables: when multiplying like bases, add the exponents. So, \(x^2 imes x^3 = x^{2+3} = x^5\) and \(y imes y^4 = y^{1+4} = y^5\).
5. Combine all parts to write the simplified expression: \(-15x^5y^5\).

Key Concepts

Multiplication of Monomials

Multiplying monomials involves multiplying their coefficients (numerical parts) and then applying the product rule to variables with exponents. This means you multiply the numbers and add the exponents of like bases.

Product Rule of Exponents

The product rule states that when multiplying two expressions with the same base, you add their exponents. For example, x^a * x^b = x^(a+b). This rule helps simplify expressions with variables raised to powers.

Handling Negative Coefficients

When multiplying coefficients, consider their signs. Multiplying a positive number by a negative number results in a negative product. This is important to determine the correct sign of the simplified expression.