Question-167966

Question Number 167966 by mathlove last updated on 30/Mar/22

Answered by HeferH last updated on 30/Mar/22

x^{x^{4}} = 4

{(x^{x^{4}})}^{4} = {(4)}^{4}

{(x^{4})}^{x^{4}} = 4^{4}

x^{4} = 4

x = \sqrt[4]{4}

x = {(2^{2})}^{\frac{1}{4}} \to 2^{\frac{1}{2}}

x = \sqrt{2}

{(\sqrt{2})}^{{(\sqrt{2})}^{8}} + {(\sqrt{2})}^{{(\sqrt{2})}^{2}} = {(2^{\frac{1}{2}})}^{16} + {(2^{\frac{1}{2}})}^{2}

{(2^{\frac{1}{2}})}^{16} + {(2^{\frac{1}{2}})}^{2} = 2^{8} + 2 = 258

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