Respuesta:
[tex]=10^{\frac{99}{100}}[/tex]
[tex]=\sqrt{\frac{a^2b^3\sqrt[15]{b^5}\sqrt[15]{c}}{d}}[/tex]
Explicación paso a paso:
[tex]\left[\sqrt[99]{\sqrt[10]{\frac{10^{10}}{\sqrt[10]{10}}}}\right]^{99}[/tex] [tex]\sqrt{\sqrt[3]{\sqrt[5]{a^{30}b^{50}cd^{-15}}}}[/tex]
[tex]=\left[\sqrt[990]{\frac{10^{10}}{\sqrt[10]{10}}}\right]^{99}[/tex] [tex]=\sqrt{\sqrt[15]{a^{30}b^{50}cd^{-15}}}[/tex]
[tex]=\left(\left(\frac{10^{10}}{\sqrt[10]{10}}\right)^{\frac{1}{990}}\right)^{99}[/tex] [tex]=\sqrt[15]{a^{30}b^{50}cd^{-15}}[/tex]
[tex]=\left(\frac{10^{10}}{\sqrt[10]{10}}\right)^{\frac{1}{990}\cdot \:99}[/tex] [tex]=\sqrt{\frac{a^2b^3\sqrt[15]{b^5}\sqrt[15]{c}}{d}}[/tex]
[tex]=\left(\frac{10^{10}}{\sqrt[10]{10}}\right)^{\frac{1}{990}\cdot \:99}[/tex]
[tex]=\sqrt[10]{\frac{10^{10}}{\sqrt[10]{10}}}[/tex]
[tex]=\frac{10}{\sqrt[100]{10}}[/tex]
[tex]=\frac{10}{10^{\frac{1}{100}}}[/tex]
[tex]=10^{1-\frac{1}{100}}[/tex]
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Verified answer
Respuesta:
[tex]=10^{\frac{99}{100}}[/tex]
[tex]=\sqrt{\frac{a^2b^3\sqrt[15]{b^5}\sqrt[15]{c}}{d}}[/tex]
Explicación paso a paso:
[tex]\left[\sqrt[99]{\sqrt[10]{\frac{10^{10}}{\sqrt[10]{10}}}}\right]^{99}[/tex] [tex]\sqrt{\sqrt[3]{\sqrt[5]{a^{30}b^{50}cd^{-15}}}}[/tex]
[tex]=\left[\sqrt[990]{\frac{10^{10}}{\sqrt[10]{10}}}\right]^{99}[/tex] [tex]=\sqrt{\sqrt[15]{a^{30}b^{50}cd^{-15}}}[/tex]
[tex]=\left(\left(\frac{10^{10}}{\sqrt[10]{10}}\right)^{\frac{1}{990}}\right)^{99}[/tex] [tex]=\sqrt[15]{a^{30}b^{50}cd^{-15}}[/tex]
[tex]=\left(\frac{10^{10}}{\sqrt[10]{10}}\right)^{\frac{1}{990}\cdot \:99}[/tex] [tex]=\sqrt{\frac{a^2b^3\sqrt[15]{b^5}\sqrt[15]{c}}{d}}[/tex]
[tex]=\left(\frac{10^{10}}{\sqrt[10]{10}}\right)^{\frac{1}{990}\cdot \:99}[/tex]
[tex]=\sqrt[10]{\frac{10^{10}}{\sqrt[10]{10}}}[/tex]
[tex]=\frac{10}{\sqrt[100]{10}}[/tex]
[tex]=\frac{10}{10^{\frac{1}{100}}}[/tex]
[tex]=10^{1-\frac{1}{100}}[/tex]
[tex]=10^{\frac{99}{100}}[/tex]