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If \(\sqrt{11\sqrt{11\sqrt{11\sqrt{11}}}}= 11^n\) what is n?

 Jul 11, 2020

Best Answer 

 #4
avatar+8336 
+1

\(\quad \sqrt{11\sqrt{11\sqrt{11\sqrt{11}}}}\\ = \sqrt{11} \cdot 11^{1/4} \cdot 11^{1/8} \cdot 11^{16}\\ = 11^{1/2 + 1/4 + 1/8 + 1/16}\\ = 11^{15/16}\)

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 Jul 11, 2020
 #1
avatar+449 
+1

hint: \(\sqrt{11}=11^{1/2}\)

 Jul 11, 2020
 #2
avatar+9770 
+1

 

What is n?

 

Hello Guest!

 

 \(11^n=\sqrt{11\sqrt{11\sqrt{11\sqrt{11}}}}= 11^{(\frac{1}{2})^{1+2+3+4}}=11^{ (\frac{1}{2})^{10}}=11^{\frac{1}{1024}}\)

 

 \(n=\frac{1}{1024}\)

laugh  !

 Jul 11, 2020
edited by asinus  Jul 11, 2020
edited by asinus  Jul 11, 2020
 #3
avatar+25880 
+2

111/2  * 111/4 * 111/8 * 111/16   =  11 15/16

 Jul 11, 2020
 #4
avatar+8336 
+1
Best Answer

\(\quad \sqrt{11\sqrt{11\sqrt{11\sqrt{11}}}}\\ = \sqrt{11} \cdot 11^{1/4} \cdot 11^{1/8} \cdot 11^{16}\\ = 11^{1/2 + 1/4 + 1/8 + 1/16}\\ = 11^{15/16}\)

MaxWong Jul 11, 2020

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