What is the value of (5.38*10^4)(4.2*10^3) in scientific notation.

First multiply the 5.38 and 4.2 together to get 22.596.  We will deal with it in a bit.  For the bases of 10, we will add the exponents giving us 10 to the 7th power.  So this is what we have so far:  .  But that decimal number has to be between 1 and 10 and it's too high so we have to move the decimal one more place to the left.  When we do that, we are adding one more power to the 10.  The final answer in scientific notation is