Question

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

Answer 1

Solution:

Given:

$(3.5\times10^{-4})(1.6\times10^{-2})$

To solve,

$\begin{gathered} (3.5\times10^{-4})(1.6\times10^{-2})=3.5\times1.6\times10^{-4}\times10^{-2} \\ =5.6\times10^{-4}\times10^{-2} \end{gathered}$

Applying the law of exponent,

$x^a\times x^b=x^{a+b}$$\begin{gathered} 5.6\times10^{-4}\times10^{-2}=5.6\times10^{-4+(-2)} \\ =5.6\times10^{-4-2} \\ =5.6\times10^{-6} \\ \text{Applying the negative law of exponent;} \\ x^{-a}=\frac{1}{x^a} \\ \\ 5.6\times10^{-6}=5.6\times\frac{1}{10^6} \\ =5.6\times\frac{1}{1000000} \\ =\frac{5.6}{1000000} \\ (3.5\times10^{-4})(1.6\times10^{-2})=0.0000056 \end{gathered}$

Therefore,

$(3.5\times10^{-4})(1.6\times10^{-2})=0.0000056$