Question 9

2(3^(3/2))

The expression 3^(5/2) - 3^(3/2) can be simplified by factoring out the common term, resulting in 2(3^(3/2)).

A) 1

This option is incorrect because the expression 3^(5/2) - 3^(3/2) simplifies to a value greater than 1. The calculation of the terms involved shows that their difference does not equal 1.

B) 2

Option B is also incorrect as the simplified expression does not evaluate to 2. Instead, the correct simplification leads to a multiple of 3^(3/2), which is significantly larger than 2.

C) 3

This choice is incorrect as well since the difference between 3^(5/2) and 3^(3/2) yields a value that is not equal to 3. The expression simplifies to a value that is dependent on 3^(3/2).

D) 3^2

Option D is incorrect because 3^2 equals 9, which is far greater than the result of the simplification of the original expression. The calculation does not support this value as a result.

E) 2(3^(3/2))

This option is correct as it accurately reflects the simplified form of the expression 3^(5/2) - 3^(3/2). By factoring out 3^(3/2), the expression simplifies to 2 times 3^(3/2), making this the correct answer.

Conclusion

The correct answer, 2(3^(3/2)), is derived from the proper simplification of the given expression. All other options fail to represent the mathematical operations involved, leading to incorrect values that do not align with the result of the subtraction. Thus, option E stands out as the definitive correct choice.