## calculusxy one year ago Scientific Notation Question!!! Question posted below...

1. calculusxy

$\huge (9 \times 10^6)^{-4}$

2. calculusxy

Write each answer in scientific notation.

3. calculusxy

@amistre64

4. anonymous

9*10^-24

5. anonymous

^ means to the power of

6. calculusxy

but wouldn't the 9 also be raised to the negative four power?

7. anonymous

no, it's basically stating that the exponents would be multiplied together

8. anonymous

the 9 is raised to the -4 as well

9. calculusxy

yes that's what i was thinking

10. calculusxy

$\frac{ 1 }{ 9^4 \times 10^{-24} }$

11. calculusxy

would that be correct?

12. jennithemeani

The 9 is also raised because it is in the exponent making it (9^-4) (10^-24)

13. jennithemeani

I don' think you are supposed to put it under 1

14. anonymous

Sense it's under Scientific notation, the only number to be raised to the power of something is usually the ten

15. anonymous

$9^{-4}\times10^{-24}=\frac{ 1 }{ 9^4\times10^{24} }$

16. anonymous

what format are you trying to write this in?

17. calculusxy

scientific notation

18. anonymous

ok then you wouldn't want to write them as fractions. keep it as $$9^{-4}\times10^{-24}$$ and evaluate 9^-4

19. calculusxy

okay so that would be like 6561

20. anonymous

1/6561 since the 4 is negative $9^{-4}=\frac{1}{6561}=1.52\times10^{-4}$ so altogether you have $1.52\times10^{-4}\times10^{-24}=1.52 \times 10^{-28}$

21. calculusxy

so we have to add 10^{-4} and 10^{-24} together? and why?

22. anonymous

because when you multiply terms with the same base you add the exponents $x^a \times x^b=x^{a+b}$

23. calculusxy

well i was trying to say that usually we would move the decimal over to a number that's larger than 10 and then multiply it by 10^{___} and the blank is like the # of times the decimal was moved over. then we multiply it with the original exponent that was given in the problem.

24. calculusxy

so i was kind of confused

25. anonymous

yeah that's the same thing, except you add it to the original exponent, not multiply

26. calculusxy

okay so if we have now: $\frac{ 4 \times 10^{-2} }{ 3.01 \times 10^{-2} }$

27. calculusxy

we would just divide them and then use the same thing that we did for this problem?

28. anonymous

yes, and since this is division, subtract the exponents

29. calculusxy

okay. can u hold on for like a minute while i try to solve the problem?

30. anonymous

sure

31. calculusxy

would it be: 1.33 x 10^0

32. anonymous

yes

33. calculusxy

thank you so much!

34. anonymous

you're welcome :)