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$${{\sqrt{{{\left({{\left({{log}_{10}\left({{\mathtt{10}}}^{\left({\mathtt{10}}\right)}\right)}^{\,{\mathtt{3}}}\right)}}^{{\mathtt{3}}}\right)}}^{{\mathtt{3}}}}}}^{\,{\mathtt{2}}}$$

solve this question

Guest May 26, 2015

Best Answer 

 #3
avatar+93650 
+5

Mmm

 

the sqrt and the square cancel each other out so the problem becomes

 

$$\{[(log_{10}(10^{10})^3]^3\}^3\\\\
=\{[(log_{10}(10^{30})]^3\}^3\\\\
=\{[30(log_{10}(10)]^3\}^3\\\\
=\{[30(1)]^3\}^3\\\\
=[30]^9\\\\
=3^9*10^9\\\\
=19683*10^9\\\\\
=1.9683*10^{13}$$

 

There you go, multiple choice answers - take your pick   

Melody  May 27, 2015
 #2
avatar+89876 
+5

 

 

log (10^(10))^3 =  (10 log 10)^3 = (10)^3  = 1000

 

1000^3 = (10^3)^3   = 10^9

 

(10^9)^3  = 10^27

 

 ([(10)^27]^2)^ (1/2)   =

 

10^27

 

 

CPhill  May 27, 2015
 #3
avatar+93650 
+5
Best Answer

Mmm

 

the sqrt and the square cancel each other out so the problem becomes

 

$$\{[(log_{10}(10^{10})^3]^3\}^3\\\\
=\{[(log_{10}(10^{30})]^3\}^3\\\\
=\{[30(log_{10}(10)]^3\}^3\\\\
=\{[30(1)]^3\}^3\\\\
=[30]^9\\\\
=3^9*10^9\\\\
=19683*10^9\\\\\
=1.9683*10^{13}$$

 

There you go, multiple choice answers - take your pick   

Melody  May 27, 2015

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