Hello I have a question about a problem. The problem is (- 25/9)^3/2. Its multiple choice however I think they are tricking us.

A. 125/27
B. - 125/27
C. 125/3
D. Not a real number

I got A as an answer but feel that it is not a real number?

NM it is D not a real number

(- 25/9)^3/2

= [(- 25/9)^3]^(1/2)
we are taking the square root of a negative number, so
no real number.

To find the value of the expression (-25/9)^(3/2), let's break it down step by step.

Step 1: Simplify the base
The negative sign in front of the fraction will stay in the result, so we can rewrite the expression as -((25/9)^(3/2)).

Step 2: Evaluate the base raised to the exponent
To do this, we need to find the square root and then the cube of the base.

Square root of 25/9: √(25/9) = √(25)/√(9) = 5/3
Cube of 5/3: (5/3)^3 = (5/3) * (5/3) * (5/3) = 125/27

Step 3: Include the negative sign from the base
Since we had a negative sign in front of the fraction, we keep it in the result.

Putting it all together, we have -((25/9)^(3/2)) = -(125/27).

Therefore, the answer is B. -125/27.

It's important to carefully check the options provided and evaluate each step of the expression to make sure the answer matches. In this case, A. 125/27 is incorrect because the expression is negative. C. 125/3 is also incorrect because the expression does not simplify to 125/3. And D. Not a real number is also incorrect because the expression can be evaluated to a real number, which is -125/27.