Question

What is the result of the mathematical expression: 22.3662720432 * (3 * 10⁸)² - (3 * 110⁸)²?

a. 2.01 x 10¹⁸
b. 6.73 x 10⁸
c. 1.2 x 10⁶
d. 3 x 10⁸

Answer 1

The result of the mathematical expression 22.3662720432 * (3 * 10⁸)² - (3 * 110⁸)² is 1.02 x 10¹⁶.

Step-by-step explanation:

To solve the mathematical expression:

22.3662720432 * (3 * 10⁸)² - (3 * 110⁸)²

We can simplify the expression step-by-step:

Step 1: Evaluate (3 * 10⁸)²

(3 * 10⁸)² = (3²) * (10⁸)² = 9 * 10¹⁶

Step 2: Evaluate (3 * 110⁸)²

(3 * 110⁸)² = (3²) * (110⁸)² = 9 * (110⁸)² = 9 * 110¹⁶

Step 3: Substitute the values into the main expression

22.3662720432 * (3 * 10⁸)² - (3 * 110⁸)² = 22.3662720432 * 9 * 10¹⁶ - 9 * 110¹⁶

Step 4: Evaluate the expression using the order of operations

22.3662720432 * 9 * 10¹⁶ - 9 * 110¹⁶ = 201.296448389 * 10¹⁶ - 9 * 110¹⁶

Step 5: Perform the multiplications

201.296448389 * 10¹⁶ - 9 * 110¹⁶ = 2012.96448389 * 10¹⁴ - 990 * 10¹⁴

Step 6: Perform the subtractions

2012.96448389 * 10¹⁴ - 990 * 10¹⁴ = 1022.96448389 * 10¹⁴

Step 7: Express the result in proper scientific notation

1022.96448389 * 10¹⁴ = 1.02 x 10¹⁶