Respuestas
Respuesta dada por:
108
b. ![\sqrt[5]{2}\sqrt[3]{5}\sqrt[6]{2^2} \sqrt[5]{2}\sqrt[3]{5}\sqrt[6]{2^2}](https://tex.z-dn.net/?f=%5Csqrt%5B5%5D%7B2%7D%5Csqrt%5B3%5D%7B5%7D%5Csqrt%5B6%5D%7B2%5E2%7D)
![=\sqrt[5]{2}\sqrt[3]{5}\sqrt[6]{2^2} =\sqrt[5]{2}\sqrt[3]{5}\sqrt[6]{2^2}](https://tex.z-dn.net/?f=%3D%5Csqrt%5B5%5D%7B2%7D%5Csqrt%5B3%5D%7B5%7D%5Csqrt%5B6%5D%7B2%5E2%7D)
(Se aplico la regla del exponente
)
![=\sqrt[5]{2}\sqrt[3]{5}\sqrt[3]{2} =\sqrt[5]{2}\sqrt[3]{5}\sqrt[3]{2}](https://tex.z-dn.net/?f=%3D%5Csqrt%5B5%5D%7B2%7D%5Csqrt%5B3%5D%7B5%7D%5Csqrt%5B3%5D%7B2%7D)
![\sqrt[5]{2}\sqrt[3]{2}=\:2^{\frac{1}{5}+\frac{1}{3}}=\:2^{\frac{8}{15}} \sqrt[5]{2}\sqrt[3]{2}=\:2^{\frac{1}{5}+\frac{1}{3}}=\:2^{\frac{8}{15}}](https://tex.z-dn.net/?f=%5Csqrt%5B5%5D%7B2%7D%5Csqrt%5B3%5D%7B2%7D%3D%5C%3A2%5E%7B%5Cfrac%7B1%7D%7B5%7D%2B%5Cfrac%7B1%7D%7B3%7D%7D%3D%5C%3A2%5E%7B%5Cfrac%7B8%7D%7B15%7D%7D)
![2^{\frac{8}{15}}\sqrt[3]{5} 2^{\frac{8}{15}}\sqrt[3]{5}](https://tex.z-dn.net/?f=2%5E%7B%5Cfrac%7B8%7D%7B15%7D%7D%5Csqrt%5B3%5D%7B5%7D)
d.![\frac{\sqrt[6]{6ab^4}}{\sqrt[3]{a^2b}} \frac{\sqrt[6]{6ab^4}}{\sqrt[3]{a^2b}}](https://tex.z-dn.net/?f=%5Cfrac%7B%5Csqrt%5B6%5D%7B6ab%5E4%7D%7D%7B%5Csqrt%5B3%5D%7Ba%5E2b%7D%7D)
Numerador:
![\sqrt[n]{ab}=\sqrt[n]{a}\sqrt[n]{b} \sqrt[n]{ab}=\sqrt[n]{a}\sqrt[n]{b}](https://tex.z-dn.net/?f=%5Csqrt%5Bn%5D%7Bab%7D%3D%5Csqrt%5Bn%5D%7Ba%7D%5Csqrt%5Bn%5D%7Bb%7D)
![\sqrt[6]{6ab^4} =\sqrt[6]{6}\sqrt[6]{a}\sqrt[6]{b^4} = \sqrt[6]{2}\sqrt[6]{3}\sqrt[6]{a}b^{\frac{2}{3}} \sqrt[6]{6ab^4} =\sqrt[6]{6}\sqrt[6]{a}\sqrt[6]{b^4} = \sqrt[6]{2}\sqrt[6]{3}\sqrt[6]{a}b^{\frac{2}{3}}](https://tex.z-dn.net/?f=%5Csqrt%5B6%5D%7B6ab%5E4%7D+%3D%5Csqrt%5B6%5D%7B6%7D%5Csqrt%5B6%5D%7Ba%7D%5Csqrt%5B6%5D%7Bb%5E4%7D+%3D+%5Csqrt%5B6%5D%7B2%7D%5Csqrt%5B6%5D%7B3%7D%5Csqrt%5B6%5D%7Ba%7Db%5E%7B%5Cfrac%7B2%7D%7B3%7D%7D)
Denominador:
![\sqrt[3]{a^2b}=\sqrt[3]{b}\sqrt[3]{a^2}=a^{\frac{2}{3}}\sqrt[3]{b} \sqrt[3]{a^2b}=\sqrt[3]{b}\sqrt[3]{a^2}=a^{\frac{2}{3}}\sqrt[3]{b}](https://tex.z-dn.net/?f=%5Csqrt%5B3%5D%7Ba%5E2b%7D%3D%5Csqrt%5B3%5D%7Bb%7D%5Csqrt%5B3%5D%7Ba%5E2%7D%3Da%5E%7B%5Cfrac%7B2%7D%7B3%7D%7D%5Csqrt%5B3%5D%7Bb%7D)
![=\frac{\sqrt[6]{2}\sqrt[6]{3}\sqrt[6]{a}b^{\frac{2}{3}}}{a^{\frac{2}{3}}\sqrt[3]{b}} =\frac{\sqrt[6]{2}\sqrt[6]{3}\sqrt[6]{a}b^{\frac{2}{3}}}{a^{\frac{2}{3}}\sqrt[3]{b}}](https://tex.z-dn.net/?f=%3D%5Cfrac%7B%5Csqrt%5B6%5D%7B2%7D%5Csqrt%5B6%5D%7B3%7D%5Csqrt%5B6%5D%7Ba%7Db%5E%7B%5Cfrac%7B2%7D%7B3%7D%7D%7D%7Ba%5E%7B%5Cfrac%7B2%7D%7B3%7D%7D%5Csqrt%5B3%5D%7Bb%7D%7D)
![=\frac{\sqrt[6]{2}\sqrt[6]{3}\sqrt[6]{a}b^{\frac{2}{3}}}{a^{\frac{2}{3}}b^{\frac{1}{3}}} =\frac{\sqrt[6]{2}\sqrt[6]{3}\sqrt[6]{a}b^{\frac{2}{3}}}{a^{\frac{2}{3}}b^{\frac{1}{3}}}](https://tex.z-dn.net/?f=%3D%5Cfrac%7B%5Csqrt%5B6%5D%7B2%7D%5Csqrt%5B6%5D%7B3%7D%5Csqrt%5B6%5D%7Ba%7Db%5E%7B%5Cfrac%7B2%7D%7B3%7D%7D%7D%7Ba%5E%7B%5Cfrac%7B2%7D%7B3%7D%7Db%5E%7B%5Cfrac%7B1%7D%7B3%7D%7D%7D)
![=\frac{\sqrt[6]{2}\sqrt[6]{3}\sqrt[6]{a}b^{\frac{1}{3}}}{a^{\frac{2}{3}}} =\frac{\sqrt[6]{2}\sqrt[6]{3}\sqrt[6]{a}b^{\frac{1}{3}}}{a^{\frac{2}{3}}}](https://tex.z-dn.net/?f=%3D%5Cfrac%7B%5Csqrt%5B6%5D%7B2%7D%5Csqrt%5B6%5D%7B3%7D%5Csqrt%5B6%5D%7Ba%7Db%5E%7B%5Cfrac%7B1%7D%7B3%7D%7D%7D%7Ba%5E%7B%5Cfrac%7B2%7D%7B3%7D%7D%7D)
![=\frac{\sqrt[6]{2}\sqrt[6]{3}\sqrt[6]{a}\sqrt[3]{b}}{a^{\frac{2}{3}}} =\frac{\sqrt[6]{2}\sqrt[6]{3}\sqrt[6]{a}\sqrt[3]{b}}{a^{\frac{2}{3}}}](https://tex.z-dn.net/?f=%3D%5Cfrac%7B%5Csqrt%5B6%5D%7B2%7D%5Csqrt%5B6%5D%7B3%7D%5Csqrt%5B6%5D%7Ba%7D%5Csqrt%5B3%5D%7Bb%7D%7D%7Ba%5E%7B%5Cfrac%7B2%7D%7B3%7D%7D%7D)
![=\frac{\sqrt[6]{6}\sqrt[6]{a}\sqrt[3]{b}}{a^{\frac{2}{3}}} =\frac{\sqrt[6]{6}\sqrt[6]{a}\sqrt[3]{b}}{a^{\frac{2}{3}}}](https://tex.z-dn.net/?f=%3D%5Cfrac%7B%5Csqrt%5B6%5D%7B6%7D%5Csqrt%5B6%5D%7Ba%7D%5Csqrt%5B3%5D%7Bb%7D%7D%7Ba%5E%7B%5Cfrac%7B2%7D%7B3%7D%7D%7D)
![=\frac{\sqrt[6]{6}\sqrt{a}\sqrt[3]{b}}{a} =\frac{\sqrt[6]{6}\sqrt{a}\sqrt[3]{b}}{a}](https://tex.z-dn.net/?f=%3D%5Cfrac%7B%5Csqrt%5B6%5D%7B6%7D%5Csqrt%7Ba%7D%5Csqrt%5B3%5D%7Bb%7D%7D%7Ba%7D)
d.
Numerador:
Denominador:
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