Answer:
[tex](1.12 x 10^5) (6.06 x 10^5) = 6.787 x 10^{10}\\[/tex]
[tex]\frac{0.5 x 10 ^ 1}{8.14 x 10 ^ 2} = 6.14 * 10 ^ {-3}\\[/tex]
Step-by-step explanation:
To solve this problem we must solve all 4 operations.
For the first one we have:
[tex](1.12 x 10^5) (6.06 x 10^5)[/tex]
When we have multiplication of powers of equal base (10) the same base is placed and the exponents are added
So:
[tex]1.12 * 6.06 x 10^{5+5} = 6.787 x 10^{10}\\[/tex]
Therefore the answer to this question is correct.
For the second question we have:
[tex](2 x 10^1) (3.0 x 10^1)[/tex]
Then following the same procedure as in the previous question we have:
[tex]2 * 3.0 x 10 ^ {1 + 1} = 6 x 10 ^ 2\\[/tex]
Then the answer shown in the statement is not correct, because 10 must be squared, product of the sum of its exponents (1 + 1)
For the third question we have:
[tex](2,775 x 10^{-4}) (4,775 x 10^4)\\2.775 * 4.775 x 10 ^{(- 4) +4} = 13.251 x10 ^ 0\\[/tex]
Then it is verified that the answer for this operation is no correct
[tex]13.25\neq 1.325[/tex]
Finally, for the fourth question we have:
[tex]\frac{5}{(8.14 x 10 ^ 2)}\\[/tex]
This we can write it as:
[tex]\frac{0.5 x 10 ^ 1}{8.14 x 10 ^ 2}\\[/tex]
In division of powers of equal base (10 in this case) the same base is placed and the exponents are subtracted:
[tex]\frac{0.5}{8.14 x 10 ^ {1-2}} = 0.0614 x 10 ^ {-1} = 6.14 * 10 ^ {-3}\\[/tex]
Finally, the problems that show correct answers are:
[tex](1.12 x 10^5) (6.06 x 10^5) = 6.787 x 10^{10}\\[/tex]
[tex]\frac{0.5 x 10 ^ 1}{8.14 x 10 ^ 2} = 6.14 * 10 ^ {-3}\\[/tex]
