To find out how many times greater \( 5 \times 10^6 \) is compared to \( 5 \times 10^2 \), you can divide the two numbers:
\[ \frac{5 \times 10^6}{5 \times 10^2} \]
The 5s in the numerator and denominator cancel out:
\[ = \frac{10^6}{10^2} \]
Using the properties of exponents, this simplifies to:
\[ = 10^{6 - 2} = 10^4 \]
Now calculate \( 10^4 \):
\[ 10^4 = 10,000 \]
Thus, \( 5 \times 10^6 \) is 10,000 times greater than \( 5 \times 10^2 \).