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How to simplify each expression & write in scientific notation?

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1 Answer

First note that since multiplication is commutative, you can the order of the numbers being multiplied without altering the final result. Also, by the associative property, the grouping of the numbers being multiplied can also be changed.

1.)    (3 · 106)(2 · 104)     ==>     (3 · 2)(10· 104)

When multiplying exponents with like bases, you keep the same base and add the exponents.

     (3 · 2)(10· 104) = (6)(106+4) = (6)(1010) = 6 · 1010

2.)     (7 · 105)3    

           ==>     (7 · 105)(7 · 105)(7 · 105= (7 · 7 · 7)(10· 10· 105)

                        = (343)(105+5+5) = (343)(1015

                        = 343 · 1015 = 3.43 · 1017 

     OR

          (7 · 105)3  =  (7)3 · (105)3  

                          =  (73) · (105·3)  =  (343) · (1015)  =  3.43 · 1017

3.)     (6 · 10-3)3(2 · 10-4)

          ==>   (6 · 10-3)3  =  (6)3 · (10-3)3  =  (63) · (10-3·3)  

                                     =  (216) · (10-9)  =  2.16 · 10-7

         (6 · 10-3)3(2 · 10-4)  

         ==>    (2.16 · 10-7)(2 · 10-4)  =  (2.16 · 2)(10-7 · 10-4)  

                       =  (4.32)(10-7+(-4))  =  (4.32)(10-11)  =  4.32 · 10-11