1. What Are Exponent Rules?

Exponent rules are mathematical rules that describe how to handle operations involving exponents. They allow us to simplify complex expressions and solve equations more easily.

2. How Does the Calculator Work?

The calculator applies standard exponent rules to simplify or expand expressions:

Explanation: The calculator parses your input expression and applies the appropriate rules based on the operation you select.

3. Common Exponent Rules

Details: The most frequently used exponent rules include:

• Product Rule: \( a^m \times a^n = a^{m+n} \)
• Quotient Rule: \( \frac{a^m}{a^n} = a^{m-n} \)
• Power Rule: \( (a^m)^n = a^{m \times n} \)
• Zero Exponent Rule: \( a^0 = 1 \)
• Negative Exponent Rule: \( a^{-n} = \frac{1}{a^n} \)

4. Using the Calculator

Tips: Enter your exponential expression using the caret (^) for exponents. For example, enter "a^2 * a^3" to see it simplified to "a^5".

5. Frequently Asked Questions (FAQ)

Q1: Can this calculator handle variables other than 'a'?
A: Yes, the calculator can work with any variable name.

Q2: What about fractional exponents?
A: The calculator follows the same rules for fractional exponents as for integer exponents.

Q3: How are negative exponents handled?
A: Negative exponents are converted to positive exponents in denominators according to the rule \( a^{-n} = \frac{1}{a^n} \).

Q4: Can I simplify expressions with different bases?
A: The calculator can only combine terms with the same base. Different bases remain separate.

Q5: What if my expression has multiple operations?
A: The calculator follows standard order of operations (PEMDAS/BODMAS) when simplifying.