Simplify each expression. See Example 1. (35m⁴n)(-2/7mn²)

Verified step by step guidance

1. Identify the expression to simplify: \((35m^4n) \times \left(-\frac{2}{7}mn^2\right)\).
2. Multiply the numerical coefficients: \$35 \times \left(-\frac{2}{7}\right)$.
3. Apply the product rule for exponents to the variables with the same base: \(m^4 \times m^1 = m^{4+1} = m^5\) and \(n^1 \times n^2 = n^{1+2} = n^3\).
4. Combine the results from the numerical multiplication and the variable multiplication to write the simplified expression.
5. Write the final simplified expression by putting together the simplified coefficient and the variables with their new exponents.

Key Concepts

Multiplication of Algebraic Expressions

Multiplying algebraic expressions involves multiplying their coefficients (numerical parts) and then applying the laws of exponents to variables. Each variable with the same base is combined by adding their exponents. This process simplifies the expression into a single term or a simpler product.

Laws of Exponents

The laws of exponents state that when multiplying like bases, you add their exponents (e.g., x^a * x^b = x^(a+b)). This rule helps simplify expressions with variables raised to powers, making it easier to combine terms and reduce the expression to its simplest form.

Multiplication of Fractions

When multiplying fractions, multiply the numerators together and the denominators together. Simplify the resulting fraction by reducing common factors. This is essential when dealing with expressions that include fractional coefficients, ensuring the final answer is in simplest form.