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# help exponents

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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