Question

Multiple. Write your answer in decimal form (3.5x10^-4)(1.6x10^-2)

Answer 1

Given:

`(3.5*10^(-4))(1.6*10^(-2))`

To solve,

`\begin{gathered} (3.5*10^(-4))(1.6*10^(-2))=3.5*1.6*10^(-4)*10^(-2) \\ =5.6*10^(-4)*10^(-2) \end{gathered}`

Applying the law of exponent,

`x^a* x^b=x^(a+b)`
`\begin{gathered} 5.6*10^(-4)*10^(-2)=5.6*10^(-4+(-2)) \\ =5.6*10^(-4-2) \\ =5.6*10^(-6) \\ \text{Applying the negative law of exponent;} \\ x^(-a)=(1)/(x^a) \\ \\ 5.6*10^(-6)=5.6*(1)/(10^6) \\ =5.6*(1)/(1000000) \\ =(5.6)/(1000000) \\ (3.5*10^(-4))(1.6*10^(-2))=0.0000056 \end{gathered}`

Therefore,

`(3.5*10^(-4))(1.6*10^(-2))=0.0000056`