Question

FINAL REVIEW HELP: multiply the scientific notation: (6 x 10^-7)(5.3 x 10^-7)

Answer 1

mult the numbers. you can re-arrange them as
\[ 6 \cdot 5.3 \cdot 10^{-7} \cdot 10^{-7} \]

Answer 2

If the final answer is out side the range 1 to 9.999, move the decimal point and adjust the exponent

Answer 3

is the answer 3.18 x 10^49

Answer 4

you add exponents.

remember 10^7 (for example) means 10*10*10*10*10*10*10
10 times itself 7 times
and
10^7 * 10^7= 10*10*10*10*10*10*10 * 10*10*10*10*10*10*10
you can count the 10's but it is easier to add 7+7=14

It still works when the 7 is -7
remember
\[ 10^{-7} \cdot 10^{-7} = \frac{1}{10^7}\cdot \frac{1}{10^7} = \frac{1}{10^7\cdot 10^{7}} \]

Answer 5

oh, so is the answer 3.18 x 10^-13

Answer 6

yes.
\[6 \cdot 5.3 \cdot 10^{-7} \cdot 10^{-7} = 31.8 \cdot 10^{-14} \]
31.8 is ≥ 10, so divide it by 10 and multiply by 10:
\[ \frac{31.8}{10} \cdot 10^{-14}\cdot 10^1 \]
which simplifies to
\[ 3.18 \cdot 10^{-13} \]