Solve the following expressions .
`(-1/(343))^(-2//3)`

Answer

To solve the expression \((-1/(343))^{-2/3}\), we will follow these steps:

### Step 1: Rewrite the expression
We start with the expression:
\[ (-1/(343))^{-2/3} \]
This can be rewritten as:
\[ \left(-\frac{1}{343}\right)^{-2/3} \]

### Step 2: Recognize the base
Next, we recognize that \(343\) is \(7^3\):
\[ \left(-\frac{1}{7^3}\right)^{-2/3} \]

### Step 3: Apply the negative exponent rule
Using the property of exponents that states \(a^{-n} = \frac{1}{a^n}\), we can rewrite the expression:
\[ \left(-\frac{1}{7^3}\right)^{-2/3} = -\frac{1}{7^3}^{-2/3} = -\left(7^3\right)^{2/3} \]

### Step 4: Simplify the exponent
Now, we simplify \((7^3)^{2/3}\) using the power of a power property, which states \((a^m)^n = a^{m \cdot n}\):
\[ (7^3)^{2/3} = 7^{3 \cdot (2/3)} = 7^2 \]

### Step 5: Calculate \(7^2\)
Now we calculate \(7^2\):
\[ 7^2 = 49 \]

### Step 6: Combine the results
Now substituting back, we have:
\[ -\left(7^2\right) = -49 \]

### Final Answer
Thus, the final answer is:
\[ \boxed{-49} \]