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 <em>adding</em> its exponents.
Rearranging the expression, we can group the exponents and coefficients together:
Multiplying each out, we notice that since
The takeaway here is that multiplying two numbers in scientific notation together has the effect of multiplying its coefficients and <em>adding</em> its exponents.