Question

Find the simplified form of the expression. Give your answer in scientific notation. (5 x 10-6)(1 x 10-3)

Answer 1

`5*10^(-9)`

Step-by-step explanation:

Given the expression:

`\mleft(5*10^(-6)\mright)\mleft(1*10^(-3)\mright)​`

First, open the brackets:

`=5*10^(-6)*1*10^(-3)`

Next, rearrange to bring like terms together:

`\begin{gathered} =5*1*10^(-6)*10^(-3) \\ =5*10^(-6)*10^(-3) \end{gathered}`

Finally, combine the powers of 10 using the addition law of indices:

`\begin{gathered} =5*10^(-6+(-3)) \\ =5*10^(-6-3) \\ =5*10^(-9)\text{ (in scientific notation)} \end{gathered}`