What is the value of $n$ such that $10^n = 10^{-6}\times \sqrt{\frac{10^{46}*10^{18}}{0.01}}$?
+2666 We have \(10^n = 10^{-6}\times \sqrt{\frac{10^{46}*10^{18}}{0.01}}\)
Recall that when you multiply exponents with the same base, you add the exponents, and when you divide exponents, you subtract the exponents.
Simplifying the square root gives us \(\sqrt{10^{64} \over {10^{-2}}}\), which can be simplified to \(\sqrt{10^{66}} = 10^{33}\).
Now we have \(10^n = 10^{-6} \times 10^{33}\).
Can you take it from here?
