1. What is the Multiplying Exponents Rule?

The exponent rule \( a^m \times b^m = (a b)^m \) shows that when multiplying terms with the same exponent but different bases, you can multiply the bases and keep the same exponent.

2. How Does the Calculator Work?

The calculator applies the exponent rule:

Where:

• \( a \) — First base (unitless)
• \( b \) — Second base (unitless)
• \( m \) — Exponent (unitless)

Explanation: This rule simplifies expressions by combining the bases while maintaining the same exponent.

3. Importance of Exponent Rules

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

4. Using the Calculator

Tips: Enter the two bases (a and b) and the common exponent (m). The calculator will show the simplified form and the calculated result.

5. Frequently Asked Questions (FAQ)

Q1: Does this rule work for different exponents?
A: No, this specific rule only applies when the exponents are identical. Different exponents require different approaches.

Q2: Can this be applied to more than two terms?
A: Yes, the rule extends to any number of terms: \( a^m \times b^m \times c^m = (a b c)^m \).

Q3: What if the bases are negative?
A: The rule still applies, but be cautious with even exponents which will make the result positive.

Q4: Does this work for fractional exponents?
A: Yes, the rule works for any real number exponent, including fractions and decimals.

Q5: How is this different from the power of a product rule?
A: This is essentially the reverse of the power of a product rule \( (ab)^m = a^m b^m \).