Question

Find the simplified form of the expression. Give your answer in scientific notation.

(9 x 10 5)(6 x 10 -7)

A. 5.4 x 10 -34

B. 1.5 x 10 -1

C. 5.4 x 10 -1

D. 1.5 x 10 -34

Answer 1

We have that exponents satisfy $a^x*a^y=a^{x+y}$
Now we get: $(9*10^5)(6*10^{-7})=9*6*10^5*10^{-7}$ by associativity of multiplication.
This is equal to: $54*10^{5+(-7)}=54*10^{-2}$ by the property we stated above, for a=10. Scientific notation requires that the coeeficient in fron tof the power of 10 is between 1-10 and thus since 54=10*5.4, we have that the expression is equal to: 5.4*10*$10^{-2}$=$5.4*10^{-1}$. Hence the correct answer is C