Comprehensive Calculator Guide
This calculator raises a number to a fractional power such as 8^(2/3) by turning it into a root and then a power: the cube root of 8 is 2, and 2 squared is 4. It handles negative exponents, and negative bases when the root is odd, so (−27)^(1/3) = −3, and shows the steps so you learn the rule, not just the answer.
The rule, negatives included
x^(m/n) = (ⁿ√x)^m: the denominator sets the root and the numerator the power. 16^(3/4) = (⁴√16)³ = 2³ = 8; the order can be swapped, but rooting first keeps numbers small.
A negative exponent means the reciprocal: 8^(−2/3) = 1/4. A negative base has a real root only for odd roots, so the calculator refuses an even denominator with a negative base.
How to Use
- Enter the base.
- Enter the exponent’s numerator and denominator (a positive whole number).
- Press “Calculate” to see the result, the root and the steps.
Formula Used
x^(m/n) = (ⁿ√x)^m
Practical Examples
- Example 1
- 8^(2/3) = (∛8)² = 4.
- Example 2
- 16^(3/4) = (⁴√16)³ = 8.
- Example 3
- (−27)^(1/3) = −3.
Important Tips
- Reduce the exponent first: 4/6 = 2/3.
Common Mistakes to Avoid
- Dividing the base by the denominator instead of taking a root.
Frequently Asked Questions
- How do I work out a fractional exponent?
- Take the root given by the denominator, then raise to the numerator.
- What is 8^(2/3)?
- 4.
- What does an exponent of 1/2 mean?
- The square root: 9^(1/2) = 3.