Simplify `(1)/((625)^(-1//4))`.

Options

A. 5
B. `1/5`
C. 25
D. `1/25`

Explanation

To simplify the expression \( \frac{1}{(625)^{-\frac{1}{4}}} \), we can follow these steps:

### Step 1: Rewrite the expression
We start with the expression:
\[ \frac{1}{(625)^{-\frac{1}{4}}} \]
Using the property of exponents that states \( a^{-n} = \frac{1}{a^n} \), we can rewrite the denominator:
\[ (625)^{-\frac{1}{4}} = \frac{1}{(625)^{\frac{1}{4}}} \]
Thus, we can rewrite the entire expression as:
\[ \frac{1}{\frac{1}{(625)^{\frac{1}{4}}}} = (625)^{\frac{1}{4}} \]

### Step 2: Evaluate \( (625)^{\frac{1}{4}} \)
Next, we need to calculate \( (625)^{\frac{1}{4}} \). We know that:
\[ 625 = 5^4 \]
So we can substitute \( 625 \) with \( 5^4 \):
\[ (625)^{\frac{1}{4}} = (5^4)^{\frac{1}{4}} \]
Using the property of exponents \( (a^m)^n = a^{m \cdot n} \), we have:
\[ (5^4)^{\frac{1}{4}} = 5^{4 \cdot \frac{1}{4}} = 5^1 = 5 \]

### Final Answer
Thus, the simplified form of \( \frac{1}{(625)^{-\frac{1}{4}}} \) is:
\[ \boxed{5} \]