Simplifying Stacked Exponents
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Your last step is incorrect, when you have $10^x10^y$, you add the exponents, so you get
$$ 10^{24 - 1,000,000,000} = 10^{-999,999,976} $$
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raindog308
Updated on December 11, 2020Comments
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raindog308 almost 3 years
I'm trying to simplify the following:
$$10^{24}(.1^{10^9})$$
I think this can be rewritten as:
$$10^{24}((10^{-1})^{10^9})$$
If memory serves (though algebra was 30 years ago) if we have stacked exponents (for example ${10^3}^{^5}$), I can simplify by multiplying the exponents (for example, ${10^3}^{^5}$ = $10^{15}$).
But this is $10^{-1}$, raised to $10^9$. Am I on the right track here, rewriting as follows:
$$10^{24}((10^{-1})^{10^9})$$ $$10^{24}((10^{-1})^{1,000,000,000})$$ $$10^{24}(10^{-1,000,000,000})$$
and then after we multiply 24 times -1,000,000,000 we get
$$10^{-24,000,000,000}$$
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Ross Millikan almost 9 yearsThe law you remember is correct if you group $10^{3^5}=\left( 10^3 \right)^5=10^{15}$. The usual convention is that $10^{3^5}$ is read as $10^{(3^5)}$ for this reason.
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raindog308 almost 9 yearsThanks for the correction!
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raindog308 almost 9 yearsD'oh! Yes you are completely right. Thank you very much.