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What is the value of $n$ such that $10^n = 10^{-5}\times \sqrt{\frac{10^{13}}{0.01}}$?

 Jul 27, 2022
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\( $10^n = 10^{-5}\times \sqrt{\frac{10^{13}}{0.01}}$\)

 

10^n  = 10^(-5)  *    sqrt ( 10^13 / (10^-2) )

 

10^n  = 10^(-5)  * sqrt (10^15) 

 

10^n   = 10^(-5)  *  (10^15)^(1/2)

 

10^n = 10^(-5)  *  10^(7.5)

 

10^n  =  10^(-5 + 7.5)

 

10^n  = 10^(2.5)

 

n = 2.5

 

 

cool cool cool

 Jul 27, 2022

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