%5E2.jpeg "(5x10^7)^2")
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.