We can multiply the whole numbers together, and then the terms with exponents together:
[tex]\sf (4.27\cdot 10^8)\cdot (9.2\cdot 10^{-5})[/tex]
[tex]\sf 4.27\cdot 9.2=39.284[/tex]
Use the exponent rule:
[tex]\sf x^a\cdot x^b\rightarrow x^{a+b}[/tex]
Which is, if you're multiplying exponents with the same base, you just add the exponents together and keep the base:
[tex]\sf 10^8\cdot 10^{-5}\rightarrow 10^{8+(-5)}\rightarrow 10^3[/tex]
So we have:
[tex]\sf 39.284\cdot 10^3=39284[/tex]
