Understanding the Basics

* Scientific Notation: A number in scientific notation is written as a *coefficient* multiplied by a power of ten. For example, 2.5 x 10^3.

* Cubing: Cubing a number means multiplying it by itself three times.

Steps

1. Cube the coefficient: Multiply the coefficient by itself three times. For example, if the coefficient is 2, 2 x 2 x 2 = 8.

2. Multiply the exponent by 3: Take the exponent in the power of ten and multiply it by 3. For example, if the exponent is 3, 3 x 3 = 9.

3. Combine the results: The cube of the number in scientific notation is the result of the cubed coefficient multiplied by 10 raised to the power of the tripled exponent.

Example:

Let's cube the number 2.5 x 10^3

1. Cube the coefficient: 2.5 x 2.5 x 2.5 = 15.625

2. Multiply the exponent by 3: 3 x 3 = 9

3. Combine: 15.625 x 10^9

Important Note:

* Adjusting for coefficient size: If the cubed coefficient is greater than or equal to 10, you'll need to adjust the coefficient and exponent to maintain the proper form of scientific notation.

* For example, if the coefficient is 15.625, you would move the decimal one place to the left (making it 1.5625) and increase the exponent by one (from 9 to 10). The final answer would be 1.5625 x 10^10.

Key Takeaway: Cubing a number in scientific notation is straightforward – cube the coefficient and triple the exponent. Just remember to adjust the coefficient and exponent if necessary to maintain the proper scientific notation format.