Simplify. Write in scientific notation:(4*10 to the 5th power)to the 2 power.

Expert Answers
kborgeson eNotes educator| Certified Educator

4000 * 10^2 is the same as 4 * 10^5, but the problem is that 4000 * 10^ 2 is no longer in scientific notation.  A number is only in scientific notation if the decimal to the number is behind the first digit of the number. 

4 * 10^5 written in standard form is 400,000, so then 4000 * 10^2 written in standard form is also 400,000.  If your instructions are to use 10^2 to write the same number you need to write it out as stated above, not in scientific notation. 

If they do not want you to take it out of scientific notation, then you may multiply (4 * 10^5)(1 * 10^-3).  That will give you 4 * 10^2, which in standard form is 400.  The other way to do the same thing is to divide  (4 * 10^5)/(1 * 10^3).  This will yield the same results as multiplying. 

In your chapter of the book you are working from you should note which way is most like the ones I have shown you.  That then will probably be the way you should work the problem.  Good Luck.  :)