Final answer:
Expressions equivalent to 9^4 are 81^2, 3^8, and (3^2)^4. These are equivalent as per the rules of exponents, where powers can be multiplied and the same base's powers can add up.
Step-by-step explanation:
To determine which expressions are equivalent to 94, we must understand how exponent rules work.
Option A: 812
Since 81 is 9 squared (92 = 81), raising 81 to the power of 2 is the same as raising 9 to the 4th power (92)2 = 94).
Option B: 38
9 is 3 squared (32 = 9), so 94 is equivalent to (32)4, which, by multiplying exponents, equals 38.
Option C: (32)4
As just explained, this is indeed equivalent to 94, because (32)4 simplifies to 32x4, which is 38.
Option D: 273
Since 27 is 3 cubed (33 = 27), raising 27 to the power of 3 is the same as raising 3 to the power of 9.
Thus, the three expressions equivalent to 94 are Options A (812), B (38), and C ((32)4).