Dividing Monomials worksheet with 20 algebraic expressions to simplify.

Let's solve each of these dividing monomials problems step by step. When dividing monomials, we follow these rules:

1. Divide the coefficients (the numbers).
2. Subtract the exponents of like bases using the rule:
$$
\frac{x^a}{x^b} = x^{a-b}
$$
3. If a variable appears in the denominator but not the numerator (or vice versa), it remains as is.

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1) $\frac{16x^2}{10x}$

- Coefficients: $\frac{16}{10} = \frac{8}{5}$
- Variables: $x^{2-1} = x^1 = x$

✔ Answer: $\boxed{\frac{8x}{5}}$

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2) $\frac{95x^8y^7}{5x^9y^2}$

- Coefficients: $\frac{95}{5} = 19$
- $x^{8-9} = x^{-1} = \frac{1}{x}$
- $y^{7-2} = y^5$

✔ Answer: $\boxed{\frac{19y^5}{x}}$

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3) $\frac{24x^4y^2}{9y^3}$

- Coefficients: $\frac{24}{9} = \frac{8}{3}$
- $x^4$: no $x$ in denominator → stays $x^4$
- $y^{2-3} = y^{-1} = \frac{1}{y}$

✔ Answer: $\boxed{\frac{8x^4}{3y}}$

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4) $\frac{9d^7}{3d^6}$

- Coefficients: $\frac{9}{3} = 3$
- $d^{7-6} = d^1 = d$

✔ Answer: $\boxed{3d}$

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5) $\frac{64x^3z^7}{40xy^4z}$

- Coefficients: $\frac{64}{40} = \frac{8}{5}$
- $x^{3-1} = x^2$
- $y^0$ in numerator? No — only $y^4$ in denominator → $y^{-4} = \frac{1}{y^4}$
- $z^{7-1} = z^6$

✔ Answer: $\boxed{\frac{8x^2z^6}{5y^4}}$

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6) $\frac{w^4u^2}{u^3}$

- $w^4$: no change
- $u^{2-3} = u^{-1} = \frac{1}{u}$

✔ Answer: $\boxed{\frac{w^4}{u}}$

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7) $\frac{x^2}{4x^4}$

- Coefficients: $\frac{1}{4}$
- $x^{2-4} = x^{-2} = \frac{1}{x^2}$

✔ Answer: $\boxed{\frac{1}{4x^2}}$

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8) $\frac{2x^3y^2}{3x^2}$

- Coefficients: $\frac{2}{3}$
- $x^{3-2} = x^1 = x$
- $y^2$: no $y$ in denominator → stays $y^2$

✔ Answer: $\boxed{\frac{2xy^2}{3}}$

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9) $\frac{3x^3}{2x^4}$

- Coefficients: $\frac{3}{2}$
- $x^{3-4} = x^{-1} = \frac{1}{x}$

✔ Answer: $\boxed{\frac{3}{2x}}$

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10) $\frac{u^4v^4}{2u^4v^4}$

- Coefficients: $\frac{1}{2}$
- $u^{4-4} = u^0 = 1$
- $v^{4-4} = v^0 = 1$

✔ Answer: $\boxed{\frac{1}{2}}$

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11) $\frac{m^4n^4}{3m^2n^6}$

- Coefficients: $\frac{1}{3}$
- $m^{4-2} = m^2$
- $n^{4-6} = n^{-2} = \frac{1}{n^2}$

✔ Answer: $\boxed{\frac{m^2}{3n^2}}$

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12) $\frac{x^4y^3}{2yx^4}$

- Coefficients: $\frac{1}{2}$
- $x^{4-4} = x^0 = 1$
- $y^{3-1} = y^2$

✔ Answer: $\boxed{\frac{y^2}{2}}$

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13) $\frac{2x^2}{3x^4y^3}$

- Coefficients: $\frac{2}{3}$
- $x^{2-4} = x^{-2} = \frac{1}{x^2}$
- $y^{-3} = \frac{1}{y^3}$

✔ Answer: $\boxed{\frac{2}{3x^2y^3}}$

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14) $\frac{4x^2}{4x^3}$

- Coefficients: $\frac{4}{4} = 1$
- $x^{2-3} = x^{-1} = \frac{1}{x}$

✔ Answer: $\boxed{\frac{1}{x}}$

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15) $\frac{3ab^4}{2a^2b^2}$

- Coefficients: $\frac{3}{2}$
- $a^{1-2} = a^{-1} = \frac{1}{a}$
- $b^{4-2} = b^2$

✔ Answer: $\boxed{\frac{3b^2}{2a}}$

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16) $\frac{2x^2}{x}$

- Coefficients: $2$
- $x^{2-1} = x^1 = x$

✔ Answer: $\boxed{2x}$

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17) $\frac{4x^2y^3}{xy^2}$

- Coefficients: $4$
- $x^{2-1} = x^1 = x$
- $y^{3-2} = y^1 = y$

✔ Answer: $\boxed{4xy}$

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18) $\frac{12p^5}{12p^4}$

- Coefficients: $\frac{12}{12} = 1$
- $p^{5-4} = p^1 = p$

✔ Answer: $\boxed{p}$

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19) $\frac{6x^3y^4}{2x^2y^3}$

- Coefficients: $\frac{6}{2} = 3$
- $x^{3-2} = x^1 = x$
- $y^{4-3} = y^1 = y$

✔ Answer: $\boxed{3xy}$

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20) $\frac{14x^4y^7}{16x^{12}y^2}$

- Coefficients: $\frac{14}{16} = \frac{7}{8}$
- $x^{4-12} = x^{-8} = \frac{1}{x^8}$
- $y^{7-2} = y^5$

✔ Answer: $\boxed{\frac{7y^5}{8x^8}}$

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✔ Final Answers Summary:

| Problem | Answer |
|--------|--------|
| 1 | $\frac{8x}{5}$ |
| 2 | $\frac{19y^5}{x}$ |
| 3 | $\frac{8x^4}{3y}$ |
| 4 | $3d$ |
| 5 | $\frac{8x^2z^6}{5y^4}$ |
| 6 | $\frac{w^4}{u}$ |
| 7 | $\frac{1}{4x^2}$ |
| 8 | $\frac{2xy^2}{3}$ |
| 9 | $\frac{3}{2x}$ |
| 10 | $\frac{1}{2}$ |
| 11 | $\frac{m^2}{3n^2}$ |
| 12 | $\frac{y^2}{2}$ |
| 13 | $\frac{2}{3x^2y^3}$ |
| 14 | $\frac{1}{x}$ |
| 15 | $\frac{3b^2}{2a}$ |
| 16 | $2x$ |
| 17 | $4xy$ |
| 18 | $p$ |
| 19 | $3xy$ |
| 20 | $\frac{7y^5}{8x^8}$ |

Let me know if you'd like this formatted as a printable worksheet or need explanations for any specific problem!