When multiplying numbers in scientific notation you blank the coefficients and substract the exponents?

For the sake of example, let's multiply the two numbers  and  together. Altogether, we have:



Rearranging the expression, we can group the exponents and coefficients together:



Multiplying each out, we notice that since and  have the same base (10), multiplying them has the effect of adding their exponents, which leaves us with:



The takeaway here is that multiplying two numbers in scientific notation together has the effect of multiplying its coefficients and adding its exponents.