Final answer:
5 x 10⁶ is 100 times larger than 5 x 10⁴. This is found by dividing the two expressions and subtracting the exponents of 10 since the base is the same.
Step-by-step explanation:
To determine how many times 5 x 10⁶ is larger than 5 x 10⁴, we can divide the former by the latter. Since the base (5) is the same for both numbers, it cancels out when we divide, leaving us to only consider the powers of 10. We get:
\(\frac{5 \times 10^6}{5 \times 10^4} = \frac{10^6}{10^4}\)
The rule for dividing exponential expressions with the same base says that we subtract the exponents. So we compute:
10² = 10^6 - 10^4
This results in 10 raised to the power of 2, which is 100. Therefore, 5 x 10⁶ is 100 times larger than 5 x 10⁴.