Which of the following is true about multiplying two exponents with the same base?

When multiplying two exponents that share the same base, the rule states that you add the exponents together. This is grounded in the properties of exponents, specifically the product of powers property, which can be expressed mathematically as follows: if you have a base 'a' and two exponents, 'm' and 'n', the equation can be written as ( a^m \times a^n = a^{m+n} ).

For instance, if you multiply ( 2^3 \times 2^4 ), you would add the exponents 3 and 4, resulting in ( 2^{3+4} = 2^7 ). This illustrates how the addition of the exponents works in practice and reinforces why this property is valid in the operation of multiplying exponents.

The other options do not align with the established rules of exponents: subtracting the exponents, multiplying the bases, or averaging the exponents do not apply when you multiply two expressions with the same base. Instead, adhering to the principle of adding the exponents ensures correct and consistent results when performing exponentiation with like bases.