Question

Please can you give me the answer in standard form​​

Answer 1

`1. (5 * 10^3) * (9 * 10^7)  = 45 * 10^(10)\\2. (7 * 10^5) / (2 * 10^2)  = 3.5 * 10^3`

Explanation:

Here, the given expressions are:

`1. (5 * 10^3) * (9 * 10^7)\\2. (7 * 10^5) / (2 * 10^2)`

Now, the LAWS OF EXPONENTS state that:

`1. a^ m * a^n = a^((m+n))\\ 2. a^m / a^n = a ^((m-n))`

Using above laws, we get:

`1. (5 * 10^3) * (9 * 10^7)\\= (5  * 9 ) * ( 10^7* 10^3)\\= 45 * (10^((7+3)))  = 45 * 10^(10)\\\implies (5 * 10^3) * (9 * 10^7)  = 45 * 10^(10)`

`2. (7 * 10^5) / (2 * 10^2)\\= ((7 * 10^5))/((2 * 10^2))  = (7)/(2)  *(10^5)/(10^2)   \\ =3.5 * 10^((5-2))  = 3.5 * 10^3\\\implies(7 * 10^5) / (2 * 10^2)  = 3.5 * 10^3`