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What is the value of $n$ such that $10^n = 10^{-6}\times \sqrt{\frac{10^{46}*10^{18}}{0.01}}$?

 Jul 4, 2022
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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?

 Jul 4, 2022

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