1. What is the Power Rule?

The power rule in mathematics states that when you raise a power to another power, you multiply the exponents. This is expressed as \((a^b)^c = a^{b \times c}\).

2. How Does the Calculator Work?

The calculator uses the power rule formula:

Where:

• \( a \) — Base number (any real number)
• \( b \) — First exponent
• \( c \) — Second exponent

Explanation: The calculator first multiplies the exponents b and c, then raises the base a to this new exponent.

3. Importance of Power Rule

Details: The power rule is fundamental in algebra and appears in various mathematical applications including polynomial operations, exponential functions, and scientific calculations.

4. Using the Calculator

Tips: Enter the base number and both exponents. All values can be positive or negative numbers, whole numbers or decimals.

5. Frequently Asked Questions (FAQ)

Q1: Does this work with negative exponents?
A: Yes, the power rule applies to all real number exponents, whether positive, negative, or fractional.

Q2: What if the base is negative?
A: Negative bases work when the final exponent is an integer. Fractional exponents of negative bases may result in complex numbers.

Q3: How precise are the calculations?
A: Results are calculated with floating-point precision and rounded to 4 decimal places.

Q4: Can I use this for scientific notation?
A: Yes, you can enter numbers in scientific notation format (like 1.23e5 for 123000).

Q5: Is there a limit to the size of numbers?
A: Extremely large numbers may return "infinity" and extremely small numbers may return 0 due to computational limits.