To simplify \((10^3) \times (10^6)\) using the power rule of exponents, which states that when multiplying two powers with the same base, you can add their exponents, you proceed as follows:
\[ 10^3 \times 10^6 = 10^{3 + 6} = 10^9 \]
So, the simplified result is:
\[ 10^9 \]