For these questions, you can isolate the (a) from the (10^x).
Example: 4 * (10^5)
a = 4
and (10^x) = (10^5)
Now, we are introduced to multiplication and divison.
We will take this as an example
4 * (10^7)
-------------
2 * (10^4)
( We will refer to the 2 as b )
First, isolate the values of a and b from the multiplier of (10^x)
4
-- = 2
2
Now we do the (10^x)
We know that when powers are "Divided", you subtract the powers.
( Example x^6 divided by x^3 ) we get x^3
Therefore, you get
10^7
------- = 10^3
10^4
You now join your values of (a/b) with your multiplier's values together and you end up with
2 * 10^3 = 2 * 10^3 = 2000
2000 is your answer.
Your working should look something like this.
a 10^x
--- * ----
b 10^y
(The y value is the second power introduced)
For multiplication, you add the power values.
(4 * 10^4) * (4 *10^6) -> It is important that you don't put the two brackets together but you put a multiplication sign in between.
You once again isolate the numbers and multiplications.
Your working should come out to be (4*4) * (10^4*10^6)
Which equals to 16 * 10^10
However, for standard form, we know that you can't have a value bigger than 1 as your number value. Therefore, we write 1.6 * 10^11.