(-2c^4d)(-4cd)

Jasonbradley

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Jun 16, 2024

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Simplifying the Expression (-2c^4d)(-4cd)

This article will guide you through the process of simplifying the expression (-2c^4d)(-4cd).

Understanding the Expression

The expression involves the multiplication of two monomials. A monomial is a single term that consists of a coefficient and variables raised to non-negative integer exponents. In this case:

• -2c^4d is a monomial where the coefficient is -2, the variable 'c' is raised to the power of 4, and the variable 'd' is raised to the power of 1 (which is usually not written).
• -4cd is another monomial with a coefficient of -4, 'c' raised to the power of 1, and 'd' raised to the power of 1.

Applying the Rules of Exponents

To simplify the expression, we need to apply the rules of exponents, specifically the product of powers rule:

x^m * x^n = x^(m+n)

This rule states that when multiplying exponents with the same base, we add their powers.

Step-by-Step Simplification

1. Multiply the coefficients: (-2) * (-4) = 8

2. Multiply the 'c' terms: c^4 * c^1 = c^(4+1) = c^5

3. Multiply the 'd' terms: d^1 * d^1 = d^(1+1) = d^2

4. Combine the results: 8 * c^5 * d^2 = 8c^5d^2

Final Result

Therefore, the simplified form of the expression (-2c^4d)(-4cd) is 8c^5d^2.