If \(\sqrt{11\sqrt{11\sqrt{11\sqrt{11}}}}= 11^n\) what is n?
\(\quad \sqrt{11\sqrt{11\sqrt{11\sqrt{11}}}}\\ = \sqrt{11} \cdot 11^{1/4} \cdot 11^{1/8} \cdot 11^{16}\\ = 11^{1/2 + 1/4 + 1/8 + 1/16}\\ = 11^{15/16}\)
hint: \(\sqrt{11}=11^{1/2}\)
What is n?
Hello Guest!
\(11^n=\sqrt{11\sqrt{11\sqrt{11\sqrt{11}}}}= 11^{(\frac{1}{2})^{1+2+3+4}}=11^{ (\frac{1}{2})^{10}}=11^{\frac{1}{1024}}\)
\(n=\frac{1}{1024}\)
!
111/2 * 111/4 * 111/8 * 111/16 = 11 15/16
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