Simplifying Stacked Exponents

2,075

Your last step is incorrect, when you have $10^x10^y$, you add the exponents, so you get

$$ 10^{24 - 1,000,000,000} = 10^{-999,999,976} $$

Share:
2,075

Related videos on Youtube

raindog308
Author by

raindog308

Updated on December 11, 2020

Comments

  • raindog308
    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

    $$10^{-24,000,000,000}$$

    • Ross Millikan
      Ross Millikan almost 9 years
      The 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.
    • raindog308
      raindog308 almost 9 years
      Thanks for the correction!
  • raindog308
    raindog308 almost 9 years
    D'oh! Yes you are completely right. Thank you very much.