Monomials multiplication worksheet with practice problems and examples.

Problem Overview:

The task involves multiplying monomials. A monomial is a single term consisting of coefficients, variables, and exponents. To multiply monomials, we follow these steps:
1. Multiply the coefficients (the numerical parts).
2. Add the exponents of the same variables.

Solution to Each Problem:

#### Problem 1:
\[
(5x^3y)(8x^4y)
\]
- Step 1: Multiply the coefficients: \(5 \times 8 = 40\).
- Step 2: Add the exponents of \(x\): \(x^3 \cdot x^4 = x^{3+4} = x^7\).
- Step 3: Add the exponents of \(y\): \(y \cdot y = y^{1+1} = y^2\).
- Answer: \(40x^7y^2\).

#### Problem 2:
\[
(7)(3xy)
\]
- Step 1: Multiply the coefficients: \(7 \times 3 = 21\).
- Step 2: The variable part remains \(xy\) since there are no other terms to combine.
- Answer: \(21xy\).

#### Problem 3:
\[
(5y)(2xy)
\]
- Step 1: Multiply the coefficients: \(5 \times 2 = 10\).
- Step 2: Add the exponents of \(x\): \(x \cdot x = x^{1+1} = x^2\).
- Step 3: Add the exponents of \(y\): \(y \cdot y = y^{1+1} = y^2\).
- Answer: \(10x^2y^2\).

#### Problem 4:
\[
(4x^2y)(6x^3y)
\]
- Step 1: Multiply the coefficients: \(4 \times 6 = 24\).
- Step 2: Add the exponents of \(x\): \(x^2 \cdot x^3 = x^{2+3} = x^5\).
- Step 3: Add the exponents of \(y\): \(y \cdot y = y^{1+1} = y^2\).
- Answer: \(24x^5y^2\).

#### Problem 5:
\[
(3x^4)x
\]
- Step 1: Multiply the coefficients: \(3 \times 1 = 3\).
- Step 2: Add the exponents of \(x\): \(x^4 \cdot x = x^{4+1} = x^5\).
- Answer: \(3x^5\).

#### Problem 6:
\[
(2x^3y)(x^2y)
\]
- Step 1: Multiply the coefficients: \(2 \times 1 = 2\).
- Step 2: Add the exponents of \(x\): \(x^3 \cdot x^2 = x^{3+2} = x^5\).
- Step 3: Add the exponents of \(y\): \(y \cdot y = y^{1+1} = y^2\).
- Answer: \(2x^5y^2\).

#### Problem 7:
\[
(13xy)(x^2y)
\]
- Step 1: Multiply the coefficients: \(13 \times 1 = 13\).
- Step 2: Add the exponents of \(x\): \(x \cdot x^2 = x^{1+2} = x^3\).
- Step 3: Add the exponents of \(y\): \(y \cdot y = y^{1+1} = y^2\).
- Answer: \(13x^3y^2\).

#### Problem 8:
\[
(6xy^2)(2x^2y)
\]
- Step 1: Multiply the coefficients: \(6 \times 2 = 12\).
- Step 2: Add the exponents of \(x\): \(x \cdot x^2 = x^{1+2} = x^3\).
- Step 3: Add the exponents of \(y\): \(y^2 \cdot y = y^{2+1} = y^3\).
- Answer: \(12x^3y^3\).

#### Problem 9:
\[
(5x^2y)(2x^3y)
\]
- Step 1: Multiply the coefficients: \(5 \times 2 = 10\).
- Step 2: Add the exponents of \(x\): \(x^2 \cdot x^3 = x^{2+3} = x^5\).
- Step 3: Add the exponents of \(y\): \(y \cdot y = y^{1+1} = y^2\).
- Answer: \(10x^5y^2\).

#### Problem 10:
\[
(xy)(xy)
\]
- Step 1: Multiply the coefficients: \(1 \times 1 = 1\).
- Step 2: Add the exponents of \(x\): \(x \cdot x = x^{1+1} = x^2\).
- Step 3: Add the exponents of \(y\): \(y \cdot y = y^{1+1} = y^2\).
- Answer: \(x^2y^2\).

Final Answers:

\[
\boxed{
\begin{array}{ll}
1. & 40x^7y^2 \\
2. & 21xy \\
3. & 10x^2y^2 \\
4. & 24x^5y^2 \\
5. & 3x^5 \\
6. & 2x^5y^2 \\
7. & 13x^3y^2 \\
8. & 12x^3y^3 \\
9. & 10x^5y^2 \\
10. & x^2y^2 \\
\end{array}
}
\]