Question

(7.5 x 10^12)÷(2.0 x 10^5)

Answer 1

Evaluate;

`(7.5*10^(12))/(2.0*10^5)`

Solution:

Re-express the expression as;

`\begin{gathered} (7.5*10^(12))/(2.0*10^5)=(75*10^(-1)*10^(12))/(2.0*10^5) \\ (7.5*10^(12))/(2.0*10^5)=(75)/(2)*(10^(11))/(10^5) \\ \end{gathered}`

Apply division law of indices;

`(a^b)/(a^c)=a^(b-c)`

`\begin{gathered} (7.5*10^(12))/(2.0*10^5)=37.5*10^(11-5) \\ (7.5*10^(12))/(2.0*10^5)=3.75*10^1*10^6 \end{gathered}`

Apply the multiplication law of indices;

`a^b* a^c=a^(b+c)`
`\begin{gathered} (7.5*10^(12))/(2.0*10^5)=3.75*10^(1+6) \\ (7.5*10^(12))/(2.0*10^5)=3.75*10^7 \\ \end{gathered}`

ANSWER:

`3.75*10^7`