Question

Select the three expressions that are equivalent to 9^4. Choose 3 answers:

A. 81^2
B. 3^8
C. (3^2)^4
D. 27^3

Answer 1

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).