Simplify each expression. See Example 1.(-4x⁵) (4x²)

Verified step by step guidance

1. Identify the coefficients and the variables in the expression: \((-4x^5)\) and \((4x^2)\).
2. Multiply the coefficients: \(-4\) and \(4\).
3. Apply the product of powers property for the variables: \(x^5\) and \(x^2\).
4. Combine the results from the previous steps: multiply the coefficients and add the exponents of the same base.
5. Write the simplified expression using the results from the previous steps.

Key Concepts

Multiplication of Monomials

Multiplying monomials involves multiplying their coefficients and adding their exponents when the bases are the same. For example, when multiplying (-4x⁵) and (4x²), you multiply -4 and 4 to get -16, and then add the exponents of x (5 + 2 = 7), resulting in -16x⁷.

Exponent Rules

Exponent rules are essential for simplifying expressions involving powers. The key rule for multiplication states that when multiplying like bases, you add the exponents. This rule is crucial for correctly simplifying expressions like (-4x⁵)(4x²) to ensure accurate results.

Combining Like Terms

Combining like terms is the process of simplifying expressions by merging terms that have the same variable raised to the same power. In the context of the given expression, after applying multiplication and exponent rules, understanding how to combine any resulting like terms is vital for achieving the simplest form of the expression.