- MODELACIÓN: Escribir las siguientes raíces en forma de potencia y simplificar cada resultado si es posible. 25. $$ \sqrt[5]{x^{5} y^{10}} $$ 26. $$ \sqrt[3]{w^{3} z^{3}} $$ 27. $$ \sqrt{4 y^{4}} $$ 28. $$ \sqrt[6]{64 x^{12} y^{6}} $$ 29. $$ \sqrt[n]{m^{2 n} x^{n}} $$ ‥1) $$ 30, \sqrt[4]{7^{8} x^{16} y^{8}} $$ 31. $$ \sqrt[10]{10^{10} x^{20}} $$ 32. $$ \sqrt[3]{27 x^{3}} $$ 33. $$ \sqrt[5]{243 x^{10}} $$

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Simplify the expression by following steps:
- step0: Solution:
  $$\left(64x^{12}y^{6}ight)^{\frac{1}{6}}$$
- step1: Use the properties of exponents:
  $$64^{\frac{1}{6}}\left(x^{12}ight)^{\frac{1}{6}}\left(y^{6}ight)^{\frac{1}{6}}$$
- step2: Evaluate the power:
  $$2x^{2}y$$
Calculate or simplify the expression $$ (7^8 * x^16 * y^8)^(1/4) $$.
Simplify the expression by following steps:
- step0: Solution:
  $$\left(7^{8}x^{16}y^{8}ight)^{\frac{1}{4}}$$
- step1: Use the properties of exponents:
  $$\left(7^{8}ight)^{\frac{1}{4}}\left(x^{16}ight)^{\frac{1}{4}}\left(y^{8}ight)^{\frac{1}{4}}$$
- step2: Evaluate the power:
  $$7^{2}x^{4}y^{2}$$
- step3: Evaluate the power:
  $$49x^{4}y^{2}$$
Calculate or simplify the expression $$ (243 * x^10)^(1/5) $$.
Simplify the expression by following steps:
- step0: Solution:
  $$\left(243x^{10}ight)^{\frac{1}{5}}$$
- step1: Use the properties of exponents:
  $$243^{\frac{1}{5}}\left(x^{10}ight)^{\frac{1}{5}}$$
- step2: Evaluate the power:
  $$3x^{2}$$
Calculate or simplify the expression $$ (w^3 * z^3)^(1/3) $$.
Simplify the expression by following steps:
- step0: Solution:
  $$\left(w^{3}z^{3}ight)^{\frac{1}{3}}$$
- step1: Use the properties of exponents:
  $$\left(w^{3}ight)^{\frac{1}{3}}\left(z^{3}ight)^{\frac{1}{3}}$$
- step2: Evaluate the power:
  $$wz$$
Calculate or simplify the expression $$ (x^5 * y^10)^(1/5) $$.
Simplify the expression by following steps:
- step0: Solution:
  $$\left(x^{5}y^{10}ight)^{\frac{1}{5}}$$
- step1: Use the properties of exponents:
  $$\left(x^{5}ight)^{\frac{1}{5}}\left(y^{10}ight)^{\frac{1}{5}}$$
- step2: Evaluate the power:
  $$xy^{2}$$
Calculate or simplify the expression $$ (10^10 * x^20)^(1/10) $$.
Simplify the expression by following steps:
- step0: Solution:
  $$\left(10^{10}x^{20}ight)^{\frac{1}{10}}$$
- step1: Use the properties of exponents:
  $$\left(10^{10}ight)^{\frac{1}{10}}\left(x^{20}ight)^{\frac{1}{10}}$$
- step2: Evaluate the power:
  $$10x^{2}$$
Calculate or simplify the expression $$ (27 * x^3)^(1/3) $$.
Simplify the expression by following steps:
- step0: Solution:
  $$\left(27x^{3}ight)^{\frac{1}{3}}$$
- step1: Use the properties of exponents:
  $$27^{\frac{1}{3}}\left(x^{3}ight)^{\frac{1}{3}}$$
- step2: Evaluate the power:
  $$3x$$
Calculate or simplify the expression $$ (4 * y^4)^(1/2) $$.
Simplify the expression by following steps:
- step0: Solution:
  $$\left(4y^{4}ight)^{\frac{1}{2}}$$
- step1: Use the properties of exponents:
  $$4^{\frac{1}{2}}\left(y^{4}ight)^{\frac{1}{2}}$$
- step2: Evaluate the power:
  $$2y^{2}$$
Calculate or simplify the expression $$ (m^(2*n) * x^n)^(1/n) $$.
Simplify the expression by following steps:
- step0: Solution:
  $$\left(m^{2n}x^{n}ight)^{\frac{1}{n}}$$
- step1: Multiply the terms:
  $$\left(\left(m^{2}xight)^{n}ight)^{\frac{1}{n}}$$
- step2: Transform the expression:
  $$\left(m^{2}xight)^{n	imes \frac{1}{n}}$$
- step3: Multiply the terms:
  $$m^{2}x$$
Aquí están las raíces escritas en forma de potencia y simplificadas:

25. $$ \sqrt[5]{x^{5} y^{10}} = xy^{2} $$

26. $$ \sqrt[3]{w^{3} z^{3}} = wz $$

27. $$ \sqrt{4 y^{4}} = 2y^{2} $$

28. $$ \sqrt[6]{64 x^{12} y^{6}} = 2x^{2}y $$

29. $$ \sqrt[n]{m^{2 n} x^{n}} = m^{2}x $$

30. $$ \sqrt[4]{7^{8} x^{16} y^{8}} = 49x^{4}y^{2} $$

31. $$ \sqrt[10]{10^{10} x^{20}} = 10x^{2} $$

32. $$ \sqrt[3]{27 x^{3}} = 3x $$

33. $$ \sqrt[5]{243 x^{10}} = 3x^{2} $$

Si necesitas más ayuda o aclaraciones, no dudes en preguntar.
Aquí están las raíces simplificadas: 25. $$ \sqrt[5]{x^{5} y^{10}} = xy^{2} $$ 26. $$ \sqrt[3]{w^{3} z^{3}} = wz $$ 27. $$ \sqrt{4 y^{4}} = 2y^{2} $$ 28. $$ \sqrt[6]{64 x^{12} y^{6}} = 2x^{2}y $$ 29. $$ \sqrt[n]{m^{2 n} x^{n}} = m^{2}x $$ 30. $$ \sqrt[4]{7^{8} x^{16} y^{8}} = 49x^{4}y^{2} $$ 31. $$ \sqrt[10]{10^{10} x^{20}} = 10x^{2} $$ 32. $$ \sqrt[3]{27 x^{3}} = 3x $$ 33. $$ \sqrt[5]{243 x^{10}} = 3x^{2} $$ Si necesitas más ayuda o aclaraciones, no dudes en preguntar.

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