Question

""Which expressions are equivalent to 6^16? Check all that apply.

a. (6^0)^16
b. (6^8)^8
c. (6^-4)^-4
d. (6^-2)^-8
e. (6^-1)^16
f. (6^8)^2

Select the expressions that are equivalent to 6^16.""

Answer 1

The expressions that are equivalent to 6^16 are b. (6^8)^8 and f. (6^8)^2 .

Explanation:

To determine which expressions are equivalent to 6^16, we can simplify each expression and compare the results to 6^16.

a. (6^0)^16 = 1^16 = 1. This expression is not equivalent to 6^16.

b. (6^8)^8 = (1679616)^8 = 281474976710656. This expression is equivalent to 6^16.

c. (6^-4)^-4 = (1/1296)^-4 = 1296^-4 = 1/1336336. This expression is not equivalent to 6^16.

d. (6^-2)^-8 = (1/36)^-8 = 36^8 = 2821109907456. This expression is not equivalent to 6^16.

e. (6^-1)^16 = (1/6)^16 = 1/281474976710656. This expression is not equivalent to 6^16.

f. (6^8)^2 = (1679616)^2 = 281474976710656. This expression is equivalent to 6^16.

From the analysis above, we can see that the expressions b. (6^8)^8 and f. (6^8)^2 are equivalent to 6^16.

Therefore, the correct expressions that are equivalent to 6^16 are b. (6^8)^8 and f. (6^8)^2.