Common power, root and fraction key signs
| Key | Purpose | Example | Result |
|---|---|---|---|
| x² | Square the current value | 15² | 225 |
| √ | Square root | √225 | 15 |
| xʸ / ^ | Raise x to any power y | 3^5 | 243 |
| x⁻¹ / 1/x | Reciprocal | 1/16 | 0.0625 |
| a b/c / n/d | Enter fractions | 2/3 + 1/6 | 5/6 |
| S⇔D / F⇔D | Fraction/decimal conversion | 3/8 ↔ decimal | 0.375 |
How to use x² and the general power key
The square key is a shortcut for exponent 2. If you need any other exponent, use xʸ, yˣ or ^ depending on the model. For 7³, enter 7, the general power key, then 3. The result is 343.
Be careful with negative bases. Mathematically, (−3)² = 9, while −3² = −9 under standard order of operations because the exponent applies before the leading negation. Parentheses remove the ambiguity.
Square roots, cube roots and nth roots
√ is the inverse of squaring. If a calculator does not provide a dedicated cube-root or nth-root key, you can use a fractional exponent:
For example, the cube root of 125 is 125^(1/3)=5. The fifth root of 32 is 32^(1/5)=2.
How fraction keys work
Many school scientific calculators provide a fraction template key such as a b/c or n/d. Some models show the fraction in textbook form; others use a linear numerator/denominator format. Enter the numerator and denominator in the template, then use the calculator's fraction/decimal conversion command if you need a decimal.
Example: adding fractions
2/3 + 1/6 = 4/6 + 1/6 = 5/6. The decimal form is approximately 0.833333….
What does 1/x or x⁻¹ mean?
The reciprocal key calculates 1 divided by the number. It is not the same as inverse sine or another inverse function. For example, the reciprocal of 8 is 1/8=0.125.
Why parentheses and order of operations matter
Scientific calculators generally follow a defined order of operations. A model may also distinguish between a negative sign and subtraction. Use parentheses when the intended grouping could be unclear.
Practice sequence for students
- Square five integers, then reverse each with √.
- Use xʸ for powers such as 2⁸, 3⁵ and 10⁻³.
- Convert three simple fractions to decimals and back where supported.
- Calculate an nth root using x^(1/n).
- Mix parentheses with powers only after the individual keys are comfortable.
Common mistakes
- Forgetting parentheses around a negative base.
- Entering 1/n incorrectly when using a fractional exponent for a root.
- Assuming a decimal approximation is more exact than a displayed fraction.
- Using the reciprocal key when the problem asks for an inverse function such as sin⁻¹.
Frequently asked questions
What key raises a number to any power?
Look for x^y, y^x, ^ or a similar power symbol. The exact label varies by model.
How do I calculate a cube root without a cube-root key?
Use x^(1/3). For example, 125^(1/3)=5.
What does x^-1 mean on a calculator?
When used as the reciprocal key, it means 1/x. This is different from inverse trigonometric notation such as sin^-1.
Why does (-3)^2 differ from -3^2?
Parentheses make -3 the base being squared. Without parentheses, standard order of operations squares 3 first and then applies the negative sign.
Open the main calculator, choose Scientific, and try the examples with your own values.