Question

Find the simplified form of the expression. Give your answer in scientific notation.

Answer 1

\[( 3 \times 10^{-6}) (6 \times 10^{-8})\]

Answer 2

These terms are multiplied together so you need to combine them using multiplication:

The factors 3 and 6 need to be multiplied together: 3 x 6 = ?
The exponents -6 and -8 need to be added together: (-6) + (-8) = ?

Answer 3

3 x 6= 18
(-6) + (-8) = -14 @jreem

Answer 4

So now you can move the factors around a little, plug in your results of 18 and -14, and get the result:
\[(3\times10^{-6})(6\times10^{-8}) = (3\times6)(10^{-6}\times10^{-8})=(18)(10^{(-6)+(-8)}) = 18\times10^{-14}\]
Does that make sense?

Answer 5

@jreem, im not understanding.. All my answers start with 1.8 or 18

Answer 6

Scientific notation means that you have to rewrite the answer so only one digit is to the left of the decimal.

So we have to turn 18 into 1.8 by extracting a 10, because (18 = 1.8 x 10)

\[18\times10^{-14}=(1.8\times10)\times10^{-14}=1.8\times(10^{1}\times10^{-14})=1.8\times10^{1+(-14)}=1.8\times10^{-13}\]

Answer 7

The end of that got chopped off, so I don't know if you can see it:
\[= 1.8\times10^{-13}\]

Answer 8

@jreem, how did you get from -14 to -13

Answer 9

It's in the previous answer. I'll break the steps into individual lines to make it easier to see.

Here's our starting point:
\[18\times10^{-14}\]
We are changing the 18 to 1.8 x 10, to make 18 into a number that has only one digit to the left of the decimal:
\[18\times10^{-14} = (1.8\times10)\times10^{-14}\]
Now we have two factors with 10 in them, so combine them:
\[(1.8\times10)\times10^{-14} = 1.8\times(10\times10^{-14})=1.8\times(10^{1}\times10^{-14})\]
We combine the factors of 10 by adding their exponents: 1 + (-14) = -13
\[1.8\times(10^1\times10^{-14})=1.8\times(10^{1+(-14)})=1.8\times(10^{-13})\]
And remove the unneeded parentheses to get the final answer:
\[1.8\times(10^{-13})=1.8\times10^{-13}\]

Answer 10

oh i see, thanks for the help and all the explianing :)

Answer 11

Happy to help :)