Final answer:
The exponent of (3^2)^4 is the result of multiplying the exponents 2 and 4, resulting in 3^8, showing that (3^2)^4 and 3^8 have the same exponent when the bases are the same.
Step-by-step explanation:
The relationship between the exponents of (3^2)^4 and the exponent of 3^8 involves the rule of exponentiation. When we raise a power to a power, we multiply the exponents. For the expression (3^2)^4, we multiply the exponent 2 by 4, resulting in an exponent of 8. Therefore, (3^2)^4 simplifies to 3^8, which directly corresponds to the exponent in 3^8. This demonstrates that the exponent of (3^2)^4 is the same as the exponent of 3^8 when the bases are the same.