Answer:
x^0/3^2 (^ means to the power) and 3x^-4. The second and last answer choices are the correct answers.
Step-by-step explanation:
1. Solve each problem by plugging in the 3. For (3/x^2)^0, plug in the 3 in replacement of x. Now it is (3/x^2)^0 (3 divided by x squared to the power of 0). 3 squared is equal to 9, and 3/9 is simplified to 1/3. Now the equation is (1/3)^0 (1/3 to the power of 0). 1/3 to the power of 3 is one because any number that has a power of 0 is equal to 1. For the first answer choice, the answer is 1, and 1 is not less the 1, it is equal to 1, so the choice wouldn't be correct.
2. In the second answer choice, x^0/3^2 (x to the power of 0/3 to the power of 2), you first have to first replace the x with a 3. The new equation would be 3^0/3^2 (3 to the power of 0 divided by 3 to the power of 2). Now we have to figure out what 3^0 (x to the power of 0). Since anything to the power of 0 is equal to 1, 3 to the power of 0 would be 1. 3 to the power of 2 is equal to 3 times 3, which equals 9. 1 divided by 9 is equal to 1/9. 1/9 is less than 1 so answer choice number 2 would be correct.
3. In the third answer choice, 1/6^-x (1 divided by 6 to the -x power), you have to plug in the 3 where the x was. Now the equation would be 1/6^-3 (1 divided by 6 to the power of -3). We have to now figure out what 6^-3 (6 to the power of -3). 6^-3 is 1/216. The equation is now 1/1/216, which equals 216, so answer choice number 3 is not correct since 216 is greater than 1 not less than 1.
4. In the fourth answer choice, 1/x^-3 (1 divided by x to the power of -3), you have to substitute x for 3. Now the equation would be 1/3^-3 (1 divided by 3 to the power of -3). Now we have to solve for 3^-3(3 to the power of -3). 3^-3 is 1/27. Now the equation is 1/1/27, which is the same as 27. 27 is not less than 1, so answer choice number four is incorrect.
5. In the fifth answer choice, 3x^-4 (3x to the power of -4), you have to first substitute x for 3. The new equation is 3 × (3^-4). According to PEMDAS, we have to first multiply 3^-4, not 3 times 3. 3^-4 (3 to the power of -4) is equal to 1/81. 3 times 1/81 is equal to 1/27. 1/27 is less than 1 so the answer is correct.
As a result, the second and last answer choices are the correct answers.
