tex]...

August 2022 1 8 Report

Знайдіть значення виразу:
[tex]1)5 {}^{( \sqrt{3} - 1) } {} {}^{2} \div (\frac{1}{5} ) {}^{2 \sqrt{3} } [/tex]
[tex]2)(( \sqrt{2} ) {}^{ \sqrt{6} } ) {}^{ \sqrt{6} } [/tex]
[tex]3)(( \sqrt[5]{10} ) {}^{ \sqrt{5} }) {} {}^{ - 2\sqrt {5} } [/tex]

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NNNLLL54

Verified answer

$1)\ \ 5^{(\sqrt3-1)^2}:\Big(\dfrac{1}{5}\Big)^{2\sqrt3}=5^{3-2\sqrt3+1}\, :\, \dfrac{1}{5^{2\sqrt3}}=5^4\cdot 5^{-2\sqrt3}\cdot \dfrac{5^{2\sqrt3}}{1}=\\\\=5^4\cdot 5^0=5^4\cdot 1=625\\\\\\2)\ \ ((\sqrt2)^{\sqrt6})^{\sqrt6}=(\sqrt2)^{\sqrt6\cdot \sqrt6}=(\sqrt2)^6=((\sqrt2)^2)^3=2^3=8$

$3)\ \ ((\sqrt[5]{10})^{\sqrt5})^{-2\sqrt5}=(\sqrt[5]{10})^{-2\cdot 5}=(\sqrt[5]{10})^{-10}=10^{-\frac{10}{5}}=10^{-2}=\dfrac{1}{100}=0,01$

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