What is 3×10 to the power of 7 times as great as 2×10 to the power of -4

On this problem, you are multiplying numbers that are in scientific notation.
3 • 10^7 multiplied by 2 • 10^-4.

To do it, you multiply the first part of each number (the mantissas) and you multiply the powers of ten part (the ordinates) of the two.

So 3 times 2 is
right... 6

Then...
10 to the seventh power    times    10 to the -4 power...
When you multiply the same base, you add the exponents...
So it is 10 to the "seven plus negative four" power.
That is 10 to the 3rd power.

So the final answer is
6 times 10 to the 3rd power.
Or
6 • 10^3