`(((625)^(-1//2))^(-1//4))^(2)=`

Options

A. 4
B. 5
C. 2
D. 3

Answer

To solve the expression \((((625)^{-1/2})^{-1/4})^{2}\), we will follow the properties of exponents step by step.

### Step 1: Rewrite the expression
We start with the expression:
\[ (((625)^{-1/2})^{-1/4})^{2} \]

### Step 2: Apply the exponent multiplication rule
Using the property of exponents that states \((a^m)^n = a^{m \cdot n}\), we can simplify the expression:
\[ (625)^{-1/2 \cdot -1/4 \cdot 2} \]

### Step 3: Calculate the exponent
Now, we calculate the exponent:
\[ -1/2 \cdot -1/4 \cdot 2 = \frac{1}{2} \cdot \frac{1}{4} \cdot 2 \]
Calculating this step-by-step:
1. \(-1/2 \cdot -1/4 = 1/8\)
2. \(1/8 \cdot 2 = 1/4\)

Thus, the exponent simplifies to:
\[ (625)^{1/4} \]

### Step 4: Simplify \(625^{1/4}\)
Next, we need to evaluate \(625^{1/4}\). We know that:
\[ 625 = 5^4 \]
Therefore:
\[ 625^{1/4} = (5^4)^{1/4} = 5^{4 \cdot 1/4} = 5^1 = 5 \]

### Final Answer
The final result of the expression \((((625)^{-1/2})^{-1/4})^{2}\) is:
\[ \boxed{5} \]