[3-4] قسمة مقدار جبري على حد جبري

اختر الإجابة الصحيحة لكل مما يأتي:

جد ناتج القسمة لكل مما يأتي:

$\begin{array}{rl}& \frac{24x^5}{12x^3}\end{array}$

• $2x^8$
• $12x^2$
• $12x^8$
• $\mathbf{2}{\mathit{x}}^{\mathbf{2}}$

$\begin{array}{rl}& \frac{36z^2{w}^2}{9zW}\end{array}$

• $4z^3{w}^3$
• $\begin{array}{rl}& \frac{1}{4}zw\end{array}$
• $\mathbf{4}\mathit{z}\mathit{w}$
• $\frac{1}{4}{z}^3{\mathrm{w}}^3$

$\begin{array}{rl}& \frac{81{\mathrm{g}}^3{\mathrm{h}}^3}{3{\mathrm{g}}^{-6}{\mathrm{h}}^{-6}}\end{array}$

• $27{\mathrm{g}}^3{\mathrm{h}}^3$
• $\begin{array}{rl}& \mathbf{27}{\mathbf{g}}^{\mathbf{9}}{\mathbf{h}}^{\mathbf{9}}\end{array}$
• $\begin{array}{rl}& 27{\mathrm{g}}^{-3}{\mathrm{h}}^{-3}\end{array}$
• $27{\mathrm{g}}^{-9}{\mathrm{h}}^{-9}$

$\begin{array}{rl}& \frac{\sqrt[3]{27}{\mathrm{m}}^5{\mathrm{n}}^5}{\sqrt[3]{8}{\mathrm{m}}^{-5}{\mathrm{n}}^{-5}}\end{array}$

• $\frac{3}{2}\mathrm{mn}$
• $\frac{3}{2}$
• $\begin{array}{rl}& \frac{\mathbf{3}}{\mathbf{2}}{\mathbf{m}}^{\mathbf{10}}{\mathbf{n}}^{\mathbf{10}}\end{array}$
• $\frac{3}{2}{m}^{-10}{n}^{-10}$

$\begin{array}{rl}& \frac{\sqrt{49}{\mathrm{x}}^{-2}{\mathrm{y}}^2}{7{\mathrm{x}}^{-3}{\mathrm{y}}^{-2}}\end{array}$

• $\mathit{x}{\mathit{y}}^{\mathbf{4}}$
• $7x^{-6}{y}^4$
• $x^{-6}{y}^4$
• $\text{xy}$

$\begin{array}{rl}& \frac{28{\mathrm{x}}^4{\mathrm{y}}^2{\mathrm{z}}^2}{\frac{1}{4}{\mathrm{x}}^3}\end{array}$

• $112x^5{y}^2{z}^2$
• $112x{y}^2{z}^2$
• $112x^{-5}{y}^2{z}^2$
• $\frac{\mathbf{112}}{\mathbf{x}}{\mathit{y}}^{\mathbf{2}}{\mathit{z}}^{\mathbf{2}}$

$\frac{48g^{-4}{h}^{-3}+12g^2{h}^2}{12g^4{h}^3}$

• $3+{\mathrm{g}}^6{\mathrm{h}}^5$
• $3{\mathrm{g}}^8{\mathrm{h}}^9+{\mathrm{g}}^2\mathrm{h}$
• $3+{\mathrm{g}}^2\mathrm{h}$
• $\mathbf{4}{\mathit{g}}^{\mathbf{-}\mathbf{8}}{\mathit{h}}^{\mathbf{-}\mathbf{6}}\mathbf{+}{\mathit{g}}^{\mathbf{-}\mathbf{2}}{\mathit{h}}^{\mathbf{-}\mathbf{1}}$

$\frac{5x^2{y}^2-15x^4{y}^2+20x^5{y}^3}{5x^3{y}^3}$

• $\begin{array}{rl}& x^5{y}^5-3x^7{y}^6+4x^2\end{array}$
• $\frac{\mathbf{1}}{\mathbf{x}\mathbf{y}}\mathbf{-}\mathbf{3}\mathit{x}{\mathit{y}}^{\mathbf{-}\mathbf{1}}\mathbf{+}\mathbf{4}{\mathit{x}}^{\mathbf{2}}$
• $\begin{array}{rl}& x^5{y}^5-3x{y}^5+4x^2{y}^6\end{array}$
• $xy-3xy+4x^{2}y$

$\frac{72z^5{w}^3+36z^6{w}^2+18z^2{w}^2}{9z^4{w}^4}$

• $8\mathrm{zw}+4{\mathrm{z}}^2{\mathrm{w}}^2+2{\mathrm{z}}^{-2}{\mathrm{w}}^{-2}$
• $8{\mathrm{zw}}^{-1}+4{\mathrm{z}}^2{\mathrm{w}}^2+2\mathrm{zw}$
• $\mathbf{8}\mathit{z}{\mathit{w}}^{\mathbf{-}\mathbf{1}}\mathbf{+}\mathbf{4}{\mathbf{z}}^{\mathbf{2}}{\mathbf{w}}^{\mathbf{-}\mathbf{2}}\mathbf{+}\mathbf{2}{\mathbf{z}}^{\mathbf{-}\mathbf{2}}{\mathbf{w}}^{\mathbf{-}\mathbf{2}}$
• $8zW+4z^2{w}^2+2z^2{w}^2$

$\frac{16m^6{n}^6-32m^7{n}^6-4m^4{n}^4}{4m^3{n}^3}$

• $4m^9{n}^9-8m^{10}{n}^9-m^7{n}^7$
• $4m^2{n}^2-8m^4{n}^3-mn$
• $4m^3{n}^3-8m^4{n}^3-m^7{n}^7$
• $\mathbf{4}{\mathit{m}}^{\mathbf{3}}{\mathit{n}}^{\mathbf{3}}\mathbf{-}\mathbf{8}{\mathit{m}}^{\mathbf{4}}{\mathit{n}}^{\mathbf{3}}\mathbf{-}\mathit{m}\mathit{n}$