A certain type of optical switch in a fiber-optic system allows a light signal to continue in one of two fibers. How many possible paths could a light signal follow if it passes through 600 such switches? The number of possible paths are (Use scientific notation. Do not round until the final answer. Then round to two decimal places as needed.)

To find the number of possible paths a light signal could follow if it passes through 600 optical switches, we need to consider that each switch has two possible outcomes (the light signal can continue in one of two fibers). Since each switch has two possible outcomes, the total number of possible paths after passing through 600 switches can be calculated using the formula for the number of possible outcomes in a series of independent events: \[ \text{Number of possible paths} = 2^{600} \] Now, we can calculate the number of possible paths using the formula above. Calculate the value by following steps: - step0: Calculate: \(2^{600}\) The number of possible paths a light signal could follow if it passes through 600 optical switches is approximately \(4.149516 \times 10^{180}\). Rounding to two decimal places, the number of possible paths is approximately \(4.15 \times 10^{180}\).