You can multiply the coefficients and powers separately:
[tex] (5 \times 10^7) \times (6 \times 10^4) = (5 \times 6) \times (10^7 \times 10^4) [/tex]
Solve the first set of parentheses:
[tex] 5 \times 6 = 30 [/tex]
Solve the second set of parentheses:
[tex] 10^7 \times 10^4 = 10^{7+4} = 10^{11} [/tex]
Now the expression can be written as follows:
[tex] 30 \times 10^{11} [/tex]
You can divide 30 by 10, so you can add one to the power for 10^11 and get your answer:
[tex] 30 \times 10^{11} = \boxed{3 \times 10^{12}} [/tex]
