Exponent Product Rule
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
\[ 2^3 \times 2^4 = 2^{3+4} = 2^7 \]\[ (2 \times 2 \times 2) \times (2 \times 2 \times 2 \times 2) = 2^7 \]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}