What is the value of $n$ such that $10^n = 10^{-6}\times \sqrt{\frac{10^{46}}{0.0001}}$
Solve for n:
10^n = sqrt(10^46/0.0001)/10^6
sqrt(10^46/0.0001)/10^6 = sqrt(10^46/(1/10000))/1000000:
10^n = sqrt(10^46/(1/10000))/1000000
10000000000000000000 = 2^19·5^19:
2^n·5^n = 2^19·5^19
Equate exponents of 2 and 5 on both sides:
n = 19 and n = 19
All equations give n = 19 as the solution:
n = 19
