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How many different values are represented by the following quantities? $$3^{-2}, 9^{-2}, 27^{-\frac{2}{3}}, 9\cdot81^{-1}, 243^{-\frac{4}{5}}$$

 Mar 3, 2020
 #1
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Sorry, can't read your LaTex !!!!

 Mar 3, 2020
 #2
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\( 3^{-2}, 9^{-2}, 27^{-\frac{2}{3}} \)     

 

3^(-2)   =  1 /3^2  =1 / 9

 

9^(-2)  = 1/9^2  = 1 / 81

 

27^(-2/3)  =    1 /  [ 27]^(2/3)  =  1 / [ 27^(1/3) ] ^2 =  1/ (3)^2  = 1/ 9

 

 

\(9\cdot81^{-1}, 243^{-\frac{4}{5}}\)

 

9 * 81^(-1)  =   9 /81 =   1/9

 

243^(-4/5)  =  1 / [ 243^(4/5) ] =   1 / [243^(1/5) ]^4  =  1/ [ 3]^4  =  1 / 81 

 

 

 

 

cool cool cool

 Mar 4, 2020

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