Questions: Multiply the monomials. - (4 x^2 y)(-2 x y^3)(5 x^4 y^2) - (4 x^2 y)(-2 x y^3)(5 x^4 y^2) = (Simplify your answer.)

Transcript text: College Algebra (4244_25Z3) ework \#14 - 11.1, 11.2 Adding & nomials, Multiplying Monomials Multiply the monomials. \[ \begin{array}{l} \left(4 x^{2} y\right)\left(-2 x y^{3}\right)\left(5 x^{4} y^{2}\right) \\ \left(4 x^{2} y\right)\left(-2 x y^{3}\right)\left(5 x^{4} y^{2}\right)= \end{array} \] (Simplify your answer.)

Solution

Solution Steps

To multiply the monomials, we need to multiply the coefficients and then apply the laws of exponents to the variables. Specifically, for each variable, we add the exponents when multiplying like bases.

Step 1: Multiply the Coefficients

We start by multiplying the coefficients of the monomials: \[ 4 \times (-2) \times 5 = -40 \]

Step 2: Add the Exponents for \(x\)

Next, we add the exponents of \(x\): \[ 2 + 1 + 4 = 7 \]

Step 3: Add the Exponents for \(y\)

Then, we add the exponents of \(y\): \[ 1 + 3 + 2 = 6 \]