25. what is (2.5 x 102)(6.3 x 105) in scientific notation? show all your work below a. 1.575 x 107 b. 1.575 x 106 c. 1.575 x 1010 d. 1.575 x 108

The correct answer is:  [A]:  " 15.75 * 10⁷ " .

The problem is:

"What is:  "(2.5 * 10²) (6.3 * 10⁵)"  (in scientific notation)?

(2.5 * 10²) (6.3 * 10⁵) =
 
 2.5 * 10² * 6.3 * 10⁵ = 

 2.5 * 6.3 * 10² * 10⁵

= 2.5 * 6.3 * 10⁽² ⁺ ⁵) = 

= 2.5 * 6.3 * 10⁷  ;

Note the following property of exponents:

xᵃ * xᵇ = x ⁽ᵃ ⁺ ᵇ⁾   ;  

Thus:  10² * 10⁵ = 10⁽² ⁺ ⁵) = 10⁷ ;

So;  we have:

2.5 * 6.3 * 10⁷ ;

→  2.5 * 6.3 * 10⁷ = (2.5 * 6.3) * 10⁷ =  15.75 * 10⁷ .

                The answer is:  [A]:  " 15.75 * 10⁷ " .