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

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

Mathematics
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\[\huge (9 \times 10^6)^{-4}\]
Write each answer in scientific notation.

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Other answers:

9*10^-24
^ means to the power of
but wouldn't the 9 also be raised to the negative four power?
no, it's basically stating that the exponents would be multiplied together
the 9 is raised to the -4 as well
yes that's what i was thinking
\[\frac{ 1 }{ 9^4 \times 10^{-24} }\]
would that be correct?
The 9 is also raised because it is in the exponent making it (9^-4) (10^-24)
I don' think you are supposed to put it under 1
Sense it's under Scientific notation, the only number to be raised to the power of something is usually the ten
\[9^{-4}\times10^{-24}=\frac{ 1 }{ 9^4\times10^{24} }\]
what format are you trying to write this in?
scientific notation
ok then you wouldn't want to write them as fractions. keep it as \(9^{-4}\times10^{-24}\) and evaluate 9^-4
okay so that would be like 6561
1/6561 since the 4 is negative \[9^{-4}=\frac{1}{6561}=1.52\times10^{-4}\] so altogether you have \[1.52\times10^{-4}\times10^{-24}=1.52 \times 10^{-28}\]
so we have to add 10^{-4} and 10^{-24} together? and why?
because when you multiply terms with the same base you add the exponents \[x^a \times x^b=x^{a+b}\]
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.
so i was kind of confused
yeah that's the same thing, except you add it to the original exponent, not multiply
okay so if we have now: \[\frac{ 4 \times 10^{-2} }{ 3.01 \times 10^{-2} }\]
we would just divide them and then use the same thing that we did for this problem?
yes, and since this is division, subtract the exponents
okay. can u hold on for like a minute while i try to solve the problem?
sure
would it be: 1.33 x 10^0
yes
thank you so much!
you're welcome :)

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