Question

How do you simplify `(5x10^2)(3x10^-3)`?

Answer 1

I assume the x's are meant as multiplication signs?

Step 1:
Multiply the numbers and the 10-powers separately:
`(5*10^2)(3*10^-3)=(5*3)(10^2*10^-3)`

Step 2:
Multiply the numbers:
`(5*3)(10^2*10^-3)=15*(10^2*10^-3)`

Step 3:
Add the powers of the 10's
`15*(10^2*10^-3)=15*(10^(2+ -3))=15*10^-1`

Step 4:
Put the negative power under the division line and simplify further:
`15*10^-1=15/10^1=15/10=1.5`
In correct scientific notation this would be `1.5*10^0`