The Exponent Product Rule states that when multiplying two expressions with the same base, you add their exponents. Mathematically, it is expressed as:

$$a^m \times a^n = a^{m+n}$$

Explanation

• ( a ) is the base.
• ( m ) and ( n ) are the exponents.
• When multiplying, you keep the base the same and add the exponents.

Example

$$2^3 \times 2^4 = 2^{3+4} = 2^7$$

Breaking it down:

$$(2 \times 2 \times 2) \times (2 \times 2 \times 2 \times 2) = 2^7$$

This rule works for any real number base (except 0) and any integer or rational exponents.

Latex

a^m \times a^n = a^{m+n}