Answer:
[tex](8 * 10^{-4}) * 0.08[/tex] = [tex]64 * 10^{-6}[/tex] = [tex]\frac{64}{10^6}[/tex] = [tex]\frac{64}{1000000}[/tex] = [tex]0.000064[/tex]
Step-by-step explanation:
Given
[tex](8 * 10^{-4}) * 0.08[/tex]
Required
Simplify
[tex](8 * 10^{-4}) * 0.08[/tex]
Express 0.08 as standard form
[tex](8 * 10^{-4}) * 8 * 10^{-2}[/tex]
Remove bracket
[tex]8 * 10^{-4} * 8 * 10^{-2}[/tex]
Apply commutative property:
[tex]8* 8 * 10^{-4} * 10^{-2}[/tex]
[tex]64 * 10^{-4} * 10^{-2}[/tex]
Apply law of indices
[tex]64 * 10^{-4-2}[/tex]
[tex]64 * 10^{-6}[/tex]
Solving further: Express [tex]10^{-6}[/tex] as fraction by applying law of indices
[tex]64 * \frac{1}{10^6}[/tex]
[tex]\frac{64}{10^6}[/tex]
[tex]10^6 = 1000000[/tex]
So, we have:
[tex]\frac{64}{1000000}[/tex]
Lastly:
[tex]0.000064[/tex]
Hence:
[tex](8 * 10^{-4}) * 0.08[/tex] = [tex]64 * 10^{-6}[/tex] = [tex]\frac{64}{10^6}[/tex] = [tex]\frac{64}{1000000}[/tex] = [tex]0.000064[/tex]
