## Understanding (5 x 10^7)^2

This expression represents the square of 5 multiplied by 10 raised to the power of 7. Let's break it down:

**5 x 10^7**: This is scientific notation representing a large number. Here, 5 is the coefficient and 10^7 represents 10 multiplied by itself 7 times (10 * 10 * 10 * 10 * 10 * 10 * 10).**Squaring**: The exponent "2" outside the parentheses means we are multiplying the entire expression within the parentheses by itself: (5 x 10^7) * (5 x 10^7).

**Calculation:**

**Multiply the coefficients**: 5 * 5 = 25**Multiply the exponents**: 10^7 * 10^7 = 10^(7+7) = 10^14

Therefore, (5 x 10^7)^2 is equivalent to **25 x 10^14**.

**Simplified Scientific Notation:**

The answer is not in proper scientific notation because the coefficient (25) is larger than 10. To adjust this, we can rewrite it as:

**2.5 x 10^15**(since we moved the decimal one place to the left, we increase the exponent by 1).

**In conclusion:**

(5 x 10^7)^2 is equal to 2.5 x 10^15. This represents a very large number - **2,500,000,000,000,000**. Understanding how to calculate and simplify such expressions is crucial in various fields like science, engineering, and computer science where dealing with large numbers is common.