Scientific Notation Question!!!
Question posted below...

- calculusxy

Scientific Notation Question!!!
Question posted below...

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- calculusxy

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

- calculusxy

Write each answer in scientific notation.

- calculusxy

@amistre64

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## More answers

- anonymous

9*10^-24

- anonymous

^ means to the power of

- calculusxy

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

- anonymous

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

- anonymous

the 9 is raised to the -4 as well

- calculusxy

yes that's what i was thinking

- calculusxy

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

- calculusxy

would that be correct?

- jennithemeani

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

- jennithemeani

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

- anonymous

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

- anonymous

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

- anonymous

what format are you trying to write this in?

- calculusxy

scientific notation

- anonymous

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

- calculusxy

okay so that would be like 6561

- anonymous

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

- calculusxy

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

- anonymous

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

- 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.

- calculusxy

so i was kind of confused

- anonymous

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

- calculusxy

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

- calculusxy

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

- anonymous

yes, and since this is division, subtract the exponents

- calculusxy

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

- anonymous

sure

- calculusxy

would it be:
1.33 x 10^0

- anonymous

yes

- calculusxy

thank you so much!

- anonymous

you're welcome :)

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