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What is the value of n such that: $$10^n = 10^{-6}\times \sqrt{\frac{10^{46}}{0.0001}}?$$

Aug 5, 2019

$$0.0001 = 10^{-4}\\ \frac{10^{46}}{10^{-4}}=10^{50}\\ \sqrt{10^{50}}=10^{25}\\10^{-6}\times 10^{25}=10^{19}\\\text{ Hence : }n=19$$