How to Calculate the Cube of a Number on a TI-30XIIS Calculator

To calculate the cube of a number (raise it to the power of 3) on your TI-30XIIS scientific calculator, you use the exponent key, typically marked with a caret (^). This function allows you to raise any number to any power, including cubing it.

Step-by-Step Guide to Cubing a Number

Follow these simple steps to cube a number on your TI-30XIIS:

Enter the Base Number: Type the number you want to cube. For example, if you want to cube 5, press 5.
Press the Exponent Key: Locate and press the ^ (caret) key. This key is often found near the top right of the numerical keypad or in the function area.
Enter the Exponent: Type 3 (for cubing).
Press Enter: Press the ENTER or = key to get your result.

Example:
To calculate 5 cubed (5³):
5 ^ 3 ENTER
The display will show 125.

Important Considerations for Negative Numbers

When cubing negative numbers, it's crucial to use parentheses to ensure the calculator applies the exponent to the entire negative number, not just its positive value.

Correct Way (Using Parentheses): To cube -3, you should enter (-3)^3. This tells the calculator to first evaluate -3, then raise that result to the third power.
- ( DRG (or (-)) 3 ) ^ 3 ENTER
- This will correctly yield -27.
Incorrect Way (Without Parentheses): If you enter -3^3 without parentheses, the calculator follows the order of operations (PEMDAS/BODMAS). It will first raise 3 to the third power (27) and then apply the negative sign, resulting in -27. However, for even powers like (-3)^2, the distinction is critical. (-3)^2 correctly yields 9, while -3^2 yields -9. Therefore, always use parentheses for negative bases to avoid misinterpretations, especially when the power could result in a positive number.

Table of Examples:

Calculation	Keystrokes (TI-30XIIS)	Result	Explanation
$4^3$	`4` `^` `3` `ENTER`	64	Basic positive cube.
$(-2)^3$	`(` `DRG` (or `(-)`) `2` `)` `^` `3` `ENTER`	-8	Correctly cubes the negative number.
$-2^3$	`DRG` (or `(-)`) `2` `^` `3` `ENTER`	-8	Calculator applies exponent first, then negative.
$7.5^3$	`7` `.` `5` `^` `3` `ENTER`	421.875	Cubing a decimal number.

By understanding the use of the ^ key and the importance of parentheses for negative numbers, you can accurately perform cubing operations and other exponentiations on your TI-30XIIS calculator. For more detailed information on your calculator's functions, always refer to the official TI-30XIIS support page.