$$ \begin{array}{lll} ext { 11. } 2 \sqrt[3]{16 x^{2} y^{7}} & ext { 17. } 2 x y \sqrt[3]{128 x^{2} y^{8}} & ext { 23. } \sqrt{8 x^{2} y^{4}+16 x y^{4}} \ ext { 12. } \frac{2}{3} \sqrt[3]{27 m^{2} n^{8}} & ext { 18. } \frac{1}{3 a} \sqrt{27 a^{3} m^{7}} & ext { 24. } \sqrt{2 x^{2}-4 x y+2 y^{2}} \ ext { 13. } 5 a \sqrt[3]{160 x^{7} y^{9} z^{13}} & ext { 19. } \frac{3}{5 x} \sqrt[3]{375 a^{8} b} & ext { 25. } \sqrt{(a-b)\left(a^{2}-b^{2} ight)} \ \begin{array}{lll} ext { 14. } \sqrt[4]{80 a^{4} b^{5} c^{12}} & ext { 20. } \frac{1}{3} \sqrt[4]{81 a^{4} b} & ext { 26. } \sqrt{2 a m^{2}+4 a m n+2 a n^{2}} \ ext { 15. } 3 \sqrt[4]{5 x^{8} y^{14} z^{16}} & ext { 21. } \sqrt{9 a+18 b} & ext { 27. } \sqrt{9 a^{3}-36 a^{2}+36 a} \ ext { 16. } \frac{25}{5} \sqrt[32 x^{2} y^{11}]{ } & ext { 22. } \sqrt{3 a^{3} b^{2}-3 a^{2} b^{2}} & \end{array}\end{array} $$

Question

$$ \begin{array}{lll}	ext { 11. } 2 \sqrt[3]{16 x^{2} y^{7}} & 	ext { 17. } 2 x y \sqrt[3]{128 x^{2} y^{8}} & 	ext { 23. } \sqrt{8 x^{2} y^{4}+16 x y^{4}} \ 	ext { 12. } \frac{2}{3} \sqrt[3]{27 m^{2} n^{8}} & 	ext { 18. } \frac{1}{3 a} \sqrt{27 a^{3} m^{7}} & 	ext { 24. } \sqrt{2 x^{2}-4 x y+2 y^{2}} \ 	ext { 13. } 5 a \sqrt[3]{160 x^{7} y^{9} z^{13}} & 	ext { 19. } \frac{3}{5 x} \sqrt[3]{375 a^{8} b} & 	ext { 25. } \sqrt{(a-b)\left(a^{2}-b^{2}ight)} \ \begin{array}{lll}	ext { 14. } \sqrt[4]{80 a^{4} b^{5} c^{12}} & 	ext { 20. } \frac{1}{3} \sqrt[4]{81 a^{4} b} & 	ext { 26. } \sqrt{2 a m^{2}+4 a m n+2 a n^{2}} \ 	ext { 15. } 3 \sqrt[4]{5 x^{8} y^{14} z^{16}} & 	ext { 21. } \sqrt{9 a+18 b} & 	ext { 27. } \sqrt{9 a^{3}-36 a^{2}+36 a} \ 	ext { 16. } \frac{25}{5} \sqrt[32 x^{2} y^{11}]{ } & 	ext { 22. } \sqrt{3 a^{3} b^{2}-3 a^{2} b^{2}} & \end{array}\end{array} $$

UpStudy AI · Accepted Answer

Vamos a simplificar cada una de las expresiones dadas paso a paso.

### 11. $$ 2 \sqrt[3]{16 x^{2} y^{7}} $$

1. **Descomponer $$16$$**: $$16 = 2^4$$.
2. **Reescribir la expresión**: 
   $$
   2 \sqrt[3]{2^4 x^2 y^7} = 2 \sqrt[3]{2^3 \cdot 2 x^2 y^6 \cdot y} = 2 \cdot 2 \sqrt[3]{2} \cdot xy^2
   $$
3. **Resultado**: 
   $$
   4xy^2 \sqrt[3]{2}
   $$

### 12. $$ \frac{2}{3} \sqrt[3]{27 m^{2} n^{8}} $$

1. **Descomponer $$27$$**: $$27 = 3^3$$.
2. **Reescribir la expresión**: 
   $$
   \frac{2}{3} \sqrt[3]{3^3 m^2 n^8} = \frac{2}{3} \cdot 3 \cdot \sqrt[3]{m^2} \cdot \sqrt[3]{n^8} = \frac{2}{3} \cdot 3 \cdot m^{\frac{2}{3}} \cdot n^{\frac{8}{3}}
   $$
3. **Resultado**: 
   $$
   2m^{\frac{2}{3}} n^{\frac{8}{3}}
   $$

### 13. $$ 5 a \sqrt[3]{160 x^{7} y^{9} z^{13}} $$

1. **Descomponer $$160$$**: $$160 = 2^5 \cdot 5$$.
2. **Reescribir la expresión**: 
   $$
   5a \sqrt[3]{2^5 \cdot 5 \cdot x^7 \cdot y^9 \cdot z^{13}} = 5a \cdot \sqrt[3]{2^3 \cdot 2^2 \cdot 5} \cdot x^{\frac{7}{3}} \cdot y^{3} \cdot z^{\frac{13}{3}}
   $$
3. **Resultado**: 
   $$
   5a \cdot 2 \cdot \sqrt[3]{10 \cdot 4} \cdot x^{\frac{7}{3}} \cdot y^{3} \cdot z^{\frac{13}{3}} = 10a y^3 x^{\frac{7}{3}} z^{\frac{13}{3}} \sqrt[3]{40}
   $$

### 14. $$ \sqrt[4]{80 a^{4} b^{5} c^{12}} $$

1. **Descomponer $$80$$**: $$80 = 16 \cdot 5 = 2^4 \cdot 5$$.
2. **Reescribir la expresión**: 
   $$
   \sqrt[4]{2^4 \cdot 5 \cdot a^4 \cdot b^5 \cdot c^{12}} = \sqrt[4]{2^4} \cdot \sqrt[4]{5} \cdot \sqrt[4]{a^4} \cdot \sqrt[4]{b^4} \cdot \sqrt[4]{b} \cdot \sqrt[4]{c^{12}}
   $$
3. **Resultado**: 
   $$
   2a b^{\frac{5}{4}} c^3 \sqrt[4]{5}
   $$

### 15. $$ 3 \sqrt[4]{5 x^{8} y^{14} z^{16}} $$

1. **Reescribir la expresión**: 
   $$
   3 \sqrt[4]{5} \cdot \sqrt[4]{x^8} \cdot \sqrt[4]{y^{14}} \cdot \sqrt[4]{z^{16}} = 3 \sqrt[4]{5} \cdot x^2 \cdot y^{\frac{14}{4}} \cdot z^4
   $$
2. **Resultado**: 
   $$
   3 \sqrt[4]{5} x^2 y^{3.5} z^4
   $$

### 16. $$ \frac{25}{5} \sqrt[32 x^{2} y^{11}]{ } $$

1. **Simplificar**: 
   $$
   5 \sqrt[3]{x^2 y^{11}} = 5 \cdot x^{\frac{2}{3}} \cdot y^{\frac{11}{3}}
   $$
2. **Resultado**: 
   $$
   5 x^{\frac{2}{3}} y^{\frac{11}{3}}
   $$

### 17. $$ 2 x y \sqrt[3]{128 x^{2} y^{8}} $$

1. **Descomponer $$128$$**: $$128 = 2^7$$.
2. **Reescribir la expresión**: 
   $$
   2xy \sqrt[3]{2^7 x^2 y^8} = 2xy \cdot 2^{\frac{7}{3}} \cdot x^{\frac{2}{3}} \cdot y^{\frac{8}{3}} = 2^{\frac{10}{3}} x^{1+\frac{2}{3}} y^{1+\frac{8}{3}}
   $$
3. **Resultado**: 
   $$
   2^{\frac{10}{3}} x^{\frac{5}{3}} y^{\frac{11}{3}}
   $$

### 18. $$ \frac{1}{3 a} \sqrt{27 a^{3} m^{7}} $$

1. **Descomponer $$27$$**: $$27 = 3^3$$.
2. **Reescribir la expresión**: 
   $$
   \frac{1}{3a} \cdot 3 \cdot a^{\frac{3}{2}} \cdot m^{\frac{7}{2}} = \frac{1}{a} a^{\frac{3}{2}} m^{\frac{7}{2}} = a^{\frac{1}{2}} m^{\frac{7}{2}}
   $$
3. **Resultado**: 
   $$
   a^{\frac{1}{2}} m^{\frac{7}{2}}
   $$

### 19. $$ \frac
11. $$ 4xy^2 \sqrt[3]{2} $$ 12. $$ 2m^{\frac{2}{3}} n^{\frac{8}{3}} $$ 13. $$ 10a y^3 x^{\frac{7}{3}} z^{\frac{13}{3}} \sqrt[3]{40} $$ 14. $$ 2a b^{\frac{5}{4}} c^3 \sqrt[4]{5} $$ 15. $$ 3 \sqrt[4]{5} x^2 y^{3.5} z^4 $$ 16. $$ 5 x^{\frac{2}{3}} y^{\frac{11}{3}} $$ 17. $$ 2^{\frac{10}{3}} x^{\frac{5}{3}} y^{\frac{11}{3}} $$ 18. $$ a^{\frac{1}{2}} m^{\frac{7}{2}} $$ 19. $$ \frac{3}{5 x} \sqrt[3]{375 a^{8} b} $$ 20. $$ \frac{1}{3} \sqrt[4]{81 a^{4} b} $$ 21. $$ \sqrt{9 a + 18 b} $$ 22. $$ \sqrt{3 a^{3} b^{2} - 3 a^{2} b^{2}} $$ 23. $$ \sqrt{8 x^{2} y^{4} + 16 x y^{4}} $$ 24. $$ \sqrt{2 x^{2} - 4 x y + 2 y^{2}} $$ 25. $$ \sqrt{(a - b)(a^{2} - b^{2})} $$ 26. $$ \sqrt{2 a m^{2} + 4 a m n + 2 a n^{2}} $$ 27. $$ \sqrt{9 a^{3} - 36 a^{2} + 36 a} $$

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19. ( \frac

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