Worksheet for practicing dividing monomials with algebraic expressions.

To solve the given problems involving dividing monomials, we need to simplify each expression by dividing the coefficients and subtracting the exponents of like bases. Let's go through each problem step by step.

Problem 1: \( 4x^2y^3 \div 2y \)

1. Divide the coefficients: \( 4 \div 2 = 2 \)
2. Subtract the exponents of \( y \): \( y^3 \div y = y^{3-1} = y^2 \)
3. The \( x \) term remains unchanged since there is no \( x \) in the divisor.
\[
4x^2y^3 \div 2y = 2x^2y^2
\]

Problem 2: \( \frac{-28x^2yz}{4yz} \)

1. Divide the coefficients: \( -28 \div 4 = -7 \)
2. Subtract the exponents of \( y \): \( y \div y = y^{1-1} = y^0 = 1 \)
3. Subtract the exponents of \( z \): \( z \div z = z^{1-1} = z^0 = 1 \)
4. The \( x \) term remains unchanged.
\[
\frac{-28x^2yz}{4yz} = -7x^2
\]

Problem 3: \( \frac{27zxy}{-3yz} \)

1. Divide the coefficients: \( 27 \div -3 = -9 \)
2. Subtract the exponents of \( y \): \( y \div y = y^{1-1} = y^0 = 1 \)
3. Subtract the exponents of \( z \): \( z \div z = z^{1-1} = z^0 = 1 \)
4. The \( x \) term remains unchanged.
\[
\frac{27zxy}{-3yz} = -9x
\]

Problem 4: \( -30xz^2 \div 3xz^2 \)

1. Divide the coefficients: \( -30 \div 3 = -10 \)
2. Subtract the exponents of \( x \): \( x \div x = x^{1-1} = x^0 = 1 \)
3. Subtract the exponents of \( z \): \( z^2 \div z^2 = z^{2-2} = z^0 = 1 \)
\[
-30xz^2 \div 3xz^2 = -10
\]

Problem 5: \( \frac{-12x^2y^4z}{2yz} \)

1. Divide the coefficients: \( -12 \div 2 = -6 \)
2. Subtract the exponents of \( y \): \( y^4 \div y = y^{4-1} = y^3 \)
3. Subtract the exponents of \( z \): \( z \div z = z^{1-1} = z^0 = 1 \)
4. The \( x \) term remains unchanged.
\[
\frac{-12x^2y^4z}{2yz} = -6x^2y^3
\]

Problem 6: \( -24x^2y^3 \div 3y \)

1. Divide the coefficients: \( -24 \div 3 = -8 \)
2. Subtract the exponents of \( y \): \( y^3 \div y = y^{3-1} = y^2 \)
3. The \( x \) term remains unchanged.
\[
-24x^2y^3 \div 3y = -8x^2y^2
\]

Problem 7: \( \frac{-14zxy}{-2yz} \)

1. Divide the coefficients: \( -14 \div -2 = 7 \)
2. Subtract the exponents of \( y \): \( y \div y = y^{1-1} = y^0 = 1 \)
3. Subtract the exponents of \( z \): \( z \div z = z^{1-1} = z^0 = 1 \)
4. The \( x \) term remains unchanged.
\[
\frac{-14zxy}{-2yz} = 7x
\]

Problem 8: \( -8xz^2 \div 4xz^2 \)

1. Divide the coefficients: \( -8 \div 4 = -2 \)
2. Subtract the exponents of \( x \): \( x \div x = x^{1-1} = x^0 = 1 \)
3. Subtract the exponents of \( z \): \( z^2 \div z^2 = z^{2-2} = z^0 = 1 \)
\[
-8xz^2 \div 4xz^2 = -2
\]

Problem 9: \( \frac{-9xyz}{-3yz} \)

1. Divide the coefficients: \( -9 \div -3 = 3 \)
2. Subtract the exponents of \( y \): \( y \div y = y^{1-1} = y^0 = 1 \)
3. Subtract the exponents of \( z \): \( z \div z = z^{1-1} = z^0 = 1 \)
4. The \( x \) term remains unchanged.
\[
\frac{-9xyz}{-3yz} = 3x
\]

Problem 10: \( -8xz^2 \div 2xz^2 \)

1. Divide the coefficients: \( -8 \div 2 = -4 \)
2. Subtract the exponents of \( x \): \( x \div x = x^{1-1} = x^0 = 1 \)
3. Subtract the exponents of \( z \): \( z^2 \div z^2 = z^{2-2} = z^0 = 1 \)
\[
-8xz^2 \div 2xz^2 = -4
\]

Problem 11: \( 6xz^2 \div 3xz^2 \)

1. Divide the coefficients: \( 6 \div 3 = 2 \)
2. Subtract the exponents of \( x \): \( x \div x = x^{1-1} = x^0 = 1 \)
3. Subtract the exponents of \( z \): \( z^2 \div z^2 = z^{2-2} = z^0 = 1 \)
\[
6xz^2 \div 3xz^2 = 2
\]

Problem 12: \( \frac{-8x^2y^3z}{2yz} \)

1. Divide the coefficients: \( -8 \div 2 = -4 \)
2. Subtract the exponents of \( y \): \( y^3 \div y = y^{3-1} = y^2 \)
3. Subtract the exponents of \( z \): \( z \div z = z^{1-1} = z^0 = 1 \)
4. The \( x \) term remains unchanged.
\[
\frac{-8x^2y^3z}{2yz} = -4x^2y^2
\]

Problem 13: \( \frac{-24zxy}{-4yz} \)

1. Divide the coefficients: \( -24 \div -4 = 6 \)
2. Subtract the exponents of \( y \): \( y \div y = y^{1-1} = y^0 = 1 \)
3. Subtract the exponents of \( z \): \( z \div z = z^{1-1} = z^0 = 1 \)
4. The \( x \) term remains unchanged.
\[
\frac{-24zxy}{-4yz} = 6x
\]

Problem 14: \( \frac{32x^2y^3z}{4yz} \)

1. Divide the coefficients: \( 32 \div 4 = 8 \)
2. Subtract the exponents of \( y \): \( y^3 \div y = y^{3-1} = y^2 \)
3. Subtract the exponents of \( z \): \( z \div z = z^{1-1} = z^0 = 1 \)
4. The \( x \) term remains unchanged.
\[
\frac{32x^2y^3z}{4yz} = 8x^2y^2
\]

Problem 15: \( -32xz^2 \div 4xz^2 \)

1. Divide the coefficients: \( -32 \div 4 = -8 \)
2. Subtract the exponents of \( x \): \( x \div x = x^{1-1} = x^0 = 1 \)
3. Subtract the exponents of \( z \): \( z^2 \div z^2 = z^{2-2} = z^0 = 1 \)
\[
-32xz^2 \div 4xz^2 = -8
\]

Problem 16: \( -8x^2y^3 \div 4y \)

1. Divide the coefficients: \( -8 \div 4 = -2 \)
2. Subtract the exponents of \( y \): \( y^3 \div y = y^{3-1} = y^2 \)
3. The \( x \) term remains unchanged.
\[
-8x^2y^3 \div 4y = -2x^2y^2
\]

Problem 17: \( 24xz^2 \div 4xz^2 \)

1. Divide the coefficients: \( 24 \div 4 = 6 \)
2. Subtract the exponents of \( x \): \( x \div x = x^{1-1} = x^0 = 1 \)
3. Subtract the exponents of \( z \): \( z^2 \div z^2 = z^{2-2} = z^0 = 1 \)
\[
24xz^2 \div 4xz^2 = 6
\]

Problem 18: \( \frac{14zxy}{-2yz} \)

1. Divide the coefficients: \( 14 \div -2 = -7 \)
2. Subtract the exponents of \( y \): \( y \div y = y^{1-1} = y^0 = 1 \)
3. Subtract the exponents of \( z \): \( z \div z = z^{1-1} = z^0 = 1 \)
4. The \( x \) term remains unchanged.
\[
\frac{14zxy}{-2yz} = -7x
\]

Problem 19: \( -9xz^2 \div 3xz^2 \)

1. Divide the coefficients: \( -9 \div 3 = -3 \)
2. Subtract the exponents of \( x \): \( x \div x = x^{1-1} = x^0 = 1 \)
3. Subtract the exponents of \( z \): \( z^2 \div z^2 = z^{2-2} = z^0 = 1 \)
\[
-9xz^2 \div 3xz^2 = -3
\]

Problem 20: \( 12xz^2 \div 3xz^2 \)

1. Divide the coefficients: \( 12 \div 3 = 4 \)
2. Subtract the exponents of \( x \): \( x \div x = x^{1-1} = x^0 = 1 \)
3. Subtract the exponents of \( z \): \( z^2 \div z^2 = z^{2-2} = z^0 = 1 \)
\[
12xz^2 \div 3xz^2 = 4
\]

Problem 21: \( 27xz^2 \div 3xz^2 \)

1. Divide the coefficients: \( 27 \div 3 = 9 \)
2. Subtract the exponents of \( x \): \( x \div x = x^{1-1} = x^0 = 1 \)
3. Subtract the exponents of \( z \): \( z^2 \div z^2 = z^{2-2} = z^0 = 1 \)
\[
27xz^2 \div 3xz^2 = 9
\]

Problem 22: \( \frac{-16x^2y^4z}{2yz} \)

1. Divide the coefficients: \( -16 \div 2 = -8 \)
2. Subtract the exponents of \( y \): \( y^4 \div y = y^{4-1} = y^3 \)
3. Subtract the exponents of \( z \): \( z \div z = z^{1-1} = z^0 = 1 \)
4. The \( x \) term remains unchanged.
\[
\frac{-16x^2y^4z}{2yz} = -8x^2y^3
\]

Final Answer:

\[
\boxed{
\begin{array}{ll}
1) & 2x^2y^2 \\
2) & -7x^2 \\
3) & -9x \\
4) & -10 \\
5) & -6x^2y^3 \\
6) & -8x^2y^2 \\
7) & 7x \\
8) & -2 \\
9) & 3x \\
10) & -4 \\
11) & 2 \\
12) & -4x^2y^2 \\
13) & 6x \\
14) & 8x^2y^2 \\
15) & -8 \\
16) & -2x^2y^2 \\
17) & 6 \\
18) & -7x \\
19) & -3 \\
20) & 4 \\
21) & 9 \\
22) & -8x^2y^3 \\
\end{array}
}
\]