Simplify each expression. See Example 8. -2⁄3 (12w) (7z)

Verified step by step guidance

1. Identify the coefficients and variables in the expression: \(-\frac{2}{3} (12w) (7z)\).
2. Multiply the coefficients: \(-\frac{2}{3} \times 12 \times 7\).
3. Combine the variables: \(w \times z\).
4. Multiply the result of the coefficients with the combined variables.
5. Simplify the expression by performing the multiplication and combining like terms.

Key Concepts

Multiplication of Fractions

When multiplying fractions, you multiply the numerators together and the denominators together. In this case, the expression involves a fraction (-2/3) multiplied by the product of two terms (12w and 7z). Understanding how to handle fractions in multiplication is essential for simplifying the expression correctly.

Distributive Property

The distributive property states that a(b + c) = ab + ac. This property is useful when simplifying expressions that involve multiplication of a term with a sum or multiple terms. In this problem, applying the distributive property helps in breaking down the multiplication of the fraction with the terms inside the parentheses.

Combining Like Terms

Combining like terms involves adding or subtracting terms that have the same variable raised to the same power. In the expression given, after simplification, it may be necessary to combine any like terms that arise. This concept is crucial for ensuring the final expression is in its simplest form.