Question

Scientific Notation Question!!!

Question posted below...

Answer 1

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

Answer 2

Write each answer in scientific notation.

Answer 3

@amistre64

Answer 4

9*10^-24

Answer 5

^ means to the power of

Answer 6

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

Answer 7

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

Answer 8

the 9 is raised to the -4 as well

Answer 9

yes that's what i was thinking

Answer 10

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

Answer 11

would that be correct?

Answer 12

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

Answer 13

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

Answer 14

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

Answer 15

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

Answer 16

what format are you trying to write this in?

Answer 17

scientific notation

Answer 18

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

Answer 19

okay so that would be like 6561

Answer 20

1/6561 since the 4 is negative

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

Answer 21

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

Answer 22

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

Answer 23

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.

Answer 24

so i was kind of confused

Answer 25

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

Answer 26

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

Answer 27

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

Answer 28

yes, and since this is division, subtract the exponents

Answer 29

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

Answer 30

sure

Answer 31

would it be:

1.33 x 10^0

Answer 32

yes

Answer 33

thank you so much!

Answer 34

you're welcome :)