[tex]a)\\x=81^{20}=(3^4)^{20}=3^{80}\\y=1024^8=(2^{10})^8=2^{80}\\x > y\\\\b)\\x=128^{36}=(2^7)^{36}=2^{252}\\y=4^{125}=(2^2)^{125}=2^{250}\\x > y\\\\c)\\x=(\frac{1}{27})^{-48}=(3^{-3})^{-48}=3^{144}\\y=243^{28}=(3^5)^{28}=3^{140}\\x > y\\\\d)\\x=(2\sqrt2)^{28}=(2\cdot2^{\frac{1}[2}})^{28}=(2^{\frac{3}{2}})^{28}=2^{42}\\y=(\frac{\sqrt8}{64})^{-6}=(\frac{8^{\frac{1}{2}}}{8^2})^{-6}=(8^{-\frac{3}{2}})^{-6}=8^9=(2^3)^9=2^{27}\\x > y[/tex]
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[tex]a)\\x=81^{20}=(3^4)^{20}=3^{80}\\y=1024^8=(2^{10})^8=2^{80}\\x > y\\\\b)\\x=128^{36}=(2^7)^{36}=2^{252}\\y=4^{125}=(2^2)^{125}=2^{250}\\x > y\\\\c)\\x=(\frac{1}{27})^{-48}=(3^{-3})^{-48}=3^{144}\\y=243^{28}=(3^5)^{28}=3^{140}\\x > y\\\\d)\\x=(2\sqrt2)^{28}=(2\cdot2^{\frac{1}[2}})^{28}=(2^{\frac{3}{2}})^{28}=2^{42}\\y=(\frac{\sqrt8}{64})^{-6}=(\frac{8^{\frac{1}{2}}}{8^2})^{-6}=(8^{-\frac{3}{2}})^{-6}=8^9=(2^3)^9=2^{27}\\x > y[/tex]