What is the property of exponents that states a^m * a^n = ?

The property of exponents that states ( a^m \times a^n = a^{m+n} ) reflects the fundamental rule of multiplying expressions with the same base. According to this property, when you multiply two powers with the same base ( a ), you simply add their exponents ( m ) and ( n ).

This can be understood by considering that multiplying the base ( a ) by itself ( m ) times and ( n ) times gives a total of ( m+n ) times. For example, if you have ( a^3 ) (which means ( a \times a \times a )) and ( a^2 ) (which means ( a \times a )), multiplying these together yields ( a \times a \times a \times a \times a = a^{3+2} = a^5 ).

Therefore, the correct answer, ( a^{m+n} ), accurately represents the result of this multiplication of like bases, confirming the additive nature of exponent properties under multiplication.