1. What is the Exponent Multiplication Rule?

The exponent multiplication rule states that when multiplying two exponential expressions with the same base, you can add the exponents while keeping the base the same. This is one of the fundamental rules of exponents in algebra.

2. How Does the Calculator Work?

The calculator uses the exponent multiplication rule:

Where:

• \( a \) — The base number
• \( m \) — The first exponent
• \( n \) — The second exponent

Explanation: This rule applies when multiplying terms with the same base. The exponents are added together while the base remains unchanged.

3. Importance of Exponent Rules

Details: Understanding exponent rules is crucial for simplifying algebraic expressions, solving equations, and working with exponential functions in mathematics and science.

4. Using the Calculator

Tips: Enter the base value and both exponents. The calculator will compute both the expanded multiplication and the simplified exponential form.

5. Frequently Asked Questions (FAQ)

Q1: Does this rule work for different bases?
A: No, this rule only applies when the bases are identical. Different bases cannot be combined using this rule.

Q2: What if the exponents are negative?
A: The rule still applies. Adding a negative exponent is equivalent to subtraction.

Q3: Can this rule be used for division?
A: For division with the same base, you subtract exponents: \( a^m ÷ a^n = a^{m-n} \).

Q4: What about fractional exponents?
A: The rule works the same way with fractional exponents. For example, \( a^{1/2} × a^{1/2} = a^{1} = a \).

Q5: Are there exceptions to this rule?
A: The main exception is when the base is 0 with negative exponents, which is undefined in mathematics.