Answer:
[tex]4 * 10^{16} or 40*10^{15}[/tex]
Step-by-step explanation:
We are given that the student has found the product of two terms which is wrong and we have to find the correct one
Value 1: [tex]8 * 10^{6} [/tex]
Value 2: [tex]5*10^9[/tex]
Product of value1 and value 2: [tex]8*10^6 * 5*10^9 = 4 * 10^{15}[/tex]
which is wrong
Error in the product:
[tex]8*10^6 * 5*10^9 = 4 * 10^{15}[/tex]
The answer with error has reduced the value by a power of 10.
They have made one of the following mistakes:
Either the product of 8*5 was written as 4 instead of 40
Or [tex] 10^6 * 10^9[/tex] was calculated as [tex]10^{14} instead of 10^{15}[/tex] because [tex]40 * 10^{14}[/tex] becomes [tex] 4 *10^ {15}[/tex]
Correct Product:
[tex]8*10^6 * 5*10^9 = 40 * 10^{15}[/tex]
Using formula: [tex]x^a * x^b = x^a+b[/tex]
[tex]10^6 * 10^9 = 10^{15}[/tex]
8*5 = 40
40 can be written as 4*10 and 10 is the same as[tex]10^1[/tex]
mulitplying them all
[tex]4 * 10 ^ 1 * 10 ^6 * 10 ^9[/tex]
[tex]= 4* 10^{16}[/tex]
which than becomes [tex]4 * 10^{16} or 40*10^{15}[/tex]
