Dividing Monomials worksheet with 20 problems to simplify algebraic expressions.

To solve these problems, we need to simplify each expression by dividing the coefficients (numbers) and subtracting the exponents of like variables. Remember the rule: when you divide powers with the same base, you subtract the exponent in the denominator from the exponent in the numerator.

Let’s go step by step for each problem:

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

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

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3)
$\frac{24x^4y^2}{9y^3}$
- Coefficients: $24 ÷ 9 = \frac{8}{3}$
- $x$: only in numerator → $x^4$
- $y$: $y^2 ÷ y^3 = y^{-1} = \frac{1}{y}$
→ Final: $\frac{8x^4}{3y}$

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4)
$\frac{9d^7}{3d^6}$
- Coefficients: $9 ÷ 3 = 3$
- $d$: $d^7 ÷ d^6 = d^1 = d$
→ Final: $3d$

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5)
$\frac{64x^2z^7}{40xy^4z}$
- Coefficients: $64 ÷ 40 = \frac{8}{5}$
- $x$: $x^2 ÷ x = x$
- $y$: only in denominator → $y^4$
- $z$: $z^7 ÷ z = z^6$
→ Final: $\frac{8xz^6}{5y^4}$

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6)
$\frac{w^4u^2}{u^3}$
- $w$: only in numerator → $w^4$
- $u$: $u^2 ÷ u^3 = u^{-1} = \frac{1}{u}$
→ Final: $\frac{w^4}{u}$

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7)
$\frac{x^3}{4x^4}$
- Coefficients: $1 ÷ 4 = \frac{1}{4}$
- $x$: $x^3 ÷ x^4 = x^{-1} = \frac{1}{x}$
→ Final: $\frac{1}{4x}$

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8)
$\frac{2x^5y^2}{3x^2}$
- Coefficients: $2 ÷ 3 = \frac{2}{3}$
- $x$: $x^5 ÷ x^2 = x^3$
- $y$: only in numerator → $y^2$
→ Final: $\frac{2x^3y^2}{3}$

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9)
$\frac{3x^2}{2x^4}$
- Coefficients: $3 ÷ 2 = \frac{3}{2}$
- $x$: $x^2 ÷ x^4 = x^{-2} = \frac{1}{x^2}$
→ Final: $\frac{3}{2x^2}$

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10)
$\frac{u^4v^4}{2u^4v^4}$
- Coefficients: $1 ÷ 2 = \frac{1}{2}$
- $u$: $u^4 ÷ u^4 = 1$
- $v$: $v^4 ÷ v^4 = 1$
→ Final: $\frac{1}{2}$

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11)
$\frac{m^4n^4}{3m^3n^4}$
- Coefficients: $1 ÷ 3 = \frac{1}{3}$
- $m$: $m^4 ÷ m^3 = m$
- $n$: $n^4 ÷ n^4 = 1$
→ Final: $\frac{m}{3}$

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12)
$\frac{x^4y^3}{2yx^4}$
- Coefficients: $1 ÷ 2 = \frac{1}{2}$
- $x$: $x^4 ÷ x^4 = 1$
- $y$: $y^3 ÷ y = y^2$
→ Final: $\frac{y^2}{2}$

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13)
$\frac{2x^2}{3x^4y^3}$
- Coefficients: $2 ÷ 3 = \frac{2}{3}$
- $x$: $x^2 ÷ x^4 = x^{-2} = \frac{1}{x^2}$
- $y$: only in denominator → $y^3$
→ Final: $\frac{2}{3x^2y^3}$

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14)
$\frac{4x^2}{4x^3}$
- Coefficients: $4 ÷ 4 = 1$
- $x$: $x^2 ÷ x^3 = x^{-1} = \frac{1}{x}$
→ Final: $\frac{1}{x}$

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15)
$\frac{3ab^4}{2a^2b^2}$
- Coefficients: $3 ÷ 2 = \frac{3}{2}$
- $a$: $a ÷ a^2 = a^{-1} = \frac{1}{a}$
- $b$: $b^4 ÷ b^2 = b^2$
→ Final: $\frac{3b^2}{2a}$

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16)
$\frac{2x^2}{x}$
- Coefficients: $2 ÷ 1 = 2$
- $x$: $x^2 ÷ x = x$
→ Final: $2x$

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17)
$\frac{4x^2y^3}{xy^2}$
- Coefficients: $4 ÷ 1 = 4$
- $x$: $x^2 ÷ x = x$
- $y$: $y^3 ÷ y^2 = y$
→ Final: $4xy$

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18)
$\frac{12p^5}{12p^4}$
- Coefficients: $12 ÷ 12 = 1$
- $p$: $p^5 ÷ p^4 = p$
→ Final: $p$

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19)
$\frac{6x^3y^4}{2x^2y^3}$
- Coefficients: $6 ÷ 2 = 3$
- $x$: $x^3 ÷ x^2 = x$
- $y$: $y^4 ÷ y^3 = y$
→ Final: $3xy$

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20)
$\frac{14x^4y^7}{16x^{12}y^2}$
- Coefficients: $14 ÷ 16 = \frac{7}{8}$
- $x$: $x^4 ÷ x^{12} = x^{-8} = \frac{1}{x^8}$
- $y$: $y^7 ÷ y^2 = y^5$
→ Final: $\frac{7y^5}{8x^8}$

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Final Answer:
1) $\frac{8x}{5}$
2) $\frac{19y^5}{x}$
3) $\frac{8x^4}{3y}$
4) $3d$
5) $\frac{8xz^6}{5y^4}$
6) $\frac{w^4}{u}$
7) $\frac{1}{4x}$
8) $\frac{2x^3y^2}{3}$
9) $\frac{3}{2x^2}$
10) $\frac{1}{2}$
11) $\frac{m}{3}$
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) $\frac{7y^5}{8x^8}$