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