6\cdot10^8 is how many times as large as 2\cdot10^{3}

To determine how many times larger \( 6 \cdot 10^8 \) is than \( 2 \cdot 10^3 \), we can set up the problem as follows:

\[
\frac{6 \cdot 10^8}{2 \cdot 10^3}
\]

We can simplify this expression step by step:

1. Divide the coefficients (the numbers in front):

\[
\frac{6}{2} = 3
\]

2. Now divide the powers of ten. When dividing powers of ten, we subtract the exponents:

\[
\frac{10^8}{10^3} = 10^{8-3} = 10^5
\]

3. Now, combine the results from steps 1 and 2:

\[
3 \cdot 10^5
\]

Thus, \( 6 \cdot 10^8 \) is \( 3 \cdot 10^5 \) times larger than \( 2 \cdot 10^3 \).

Final answer:

\[
6 \cdot 10^8 \text{ is } 3 \cdot 10^5 \text{ times as large as } 2 \cdot 10^3.
\]