(2.5×10−10)(7×10−6)

express your answer in scientific notation.

a. 1.75×1016

b. 1.75×10−15

c. 1.75×10−16

d. 1.75×10−17

The answer is:  [B]:  " 1.75 * 10⁻¹⁵ " .

Note:

(2.5 * 10⁻¹⁰)(7 * 10⁻⁶) = (2.5)*(7) *(10⁻¹⁰) *(10⁻⁶)

Note:  (10⁻¹⁰) *(10⁻⁶) = 10⁽⁻¹⁰⁾⁺⁽⁻⁶⁾ = 10⁽⁻¹⁰⁻⁶⁾ = 10⁽⁻¹⁶⁾

{Note:  xᵃ * xᵇ = x⁽ᵃ⁺ᵇ⁾ } ;  ===> Property of exponents; 

So;   (2.5)*(7) *(10⁻¹⁰) *(10⁻⁶) = (2.5)*(7) * 10⁽⁻¹⁶⁾ ;

   2.5 * 7 = 17.5 ;

so; (2.5)*(7) * 10⁽⁻¹⁶⁾ = 17.5 * 10⁻¹⁶

SInce the answer choices are given in scientific notation; 
 in terms of "1.75"; we rewrite this value in such format to get the equivalent value; by dividing by "10" ; to get:  "1.75 * 10⁻¹⁵ "  (note: this value is equivalent; since the number of "zeros" is adjusted.

The answer is:  [B]:  " 1.75 * 10⁻¹⁵ " .
 

Answers: the graph is translated down 1 unit and the domain and range of g(x) is the same as the domain and range of f(x).

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