Alegbra 1 (mutilpying powers with the same base)

Question

A human body contains about 2.7x104 microliters (ml) of blood for each pound of body weight. Each microliter of blood contains about 7x104 white blood cells. About how many white blood cells are in the body of a 140-lb person.

Answer 1

The Rule said :   aⁿ x  a^m = a^{n +m}         

where a -  the base .     m, n -  exponents  or powers.

step 1 Lets to  find how many white blood cells contain 1lb of body. 

If  one lb contain 2.7 x 10⁴ ml  and  every ml  contain 7 x 10⁴ white blood cells, then

1lb contain  (2.7 x 7)  x 10⁴⁺⁴   or  18.9 x 10⁸  white blood cells.

 step 2 If  1lb contain 18.9 x 10⁸  white blood cells,  then multiplication by number of pounds ( weight)   will give the total number of white blood cells. 

 Find for W =  140 lb  :   140  x  18.9 x 10⁸ =  2646 x 10⁸  = 2. 646 x 10¹¹   ( make smaller number by increases the  power)    

Answer 2

Looks like a 2-stage simple multiplication.  Let's ignore the 10⁴'s for now to make it easier:

We have 140 total lbs X ml for each pound:  140 X 2.7 = 378 ml (X 10⁴) in this dude (or dudette).

And 378 ml X # white cells = 378 X 7 = 2,646 total white blood cells/140 pounds, times 10⁴ times 10⁴.

How do we handle exponents when multiplying terms?  We add them, so 10⁴ times 10⁴ = 10⁴⁺⁴ = 10⁸

Now we have 2646 X 10⁸, which = 2.646 X 10¹¹   (since we moved the decimal to make a smaller number, the exponent count increases)