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Question Number 19785 by Tinkutara last updated on 15/Aug/17

$$\mathrm{If}{x}^{\left(x^4\right)}=4,\mathrm{what}\mathrm{is}\mathrm{the}\mathrm{value}\mathrm{of}$$$$x^{\left(x^2\right)}+x^{\left(x^8\right)}?$$

Answered by Tinkutara last updated on 16/Aug/17

$$\mathrm{Let}x=y^{\frac{1}{4}}\Rightarrow x^4=y$$$$y^{\frac{y}{4}}=4$$$$y^y=4^4\Rightarrow y=4\Rightarrow x=\sqrt{2}$$

Commented by ajfour last updated on 16/Aug/17

$$\mathrm{very}\mathrm{nice}\mathrm{trick}.$$

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