Find the value of `((2)/(3))^(-4//5)`.

Answer

To find the value of \(\left(\frac{2}{3}\right)^{-\frac{4}{5}}\), we can follow these steps:

### Step 1: Apply the Negative Exponent Rule
The negative exponent rule states that \(x^{-y} = \frac{1}{x^y}\). Here, we have:
\[ \left(\frac{2}{3}\right)^{-\frac{4}{5}} = \frac{1}{\left(\frac{2}{3}\right)^{\frac{4}{5}}} \]

### Step 2: Rewrite the Fraction
We can rewrite the fraction \(\frac{2}{3}\) in the exponent:
\[ \frac{1}{\left(\frac{2}{3}\right)^{\frac{4}{5}}} = \frac{1}{\left(\frac{2}{3}\right)^{\frac{4}{5}}} = \frac{1}{\left(\frac{2^4}{3^4}\right)^{\frac{1}{5}}} \]

### Step 3: Simplify the Exponent
Now, we can simplify \(\left(\frac{2^4}{3^4}\right)^{\frac{1}{5}}\):
\[ \left(\frac{2^4}{3^4}\right)^{\frac{1}{5}} = \frac{2^{\frac{4}{5}}}{3^{\frac{4}{5}}} \]

### Step 4: Substitute Back
Now, substituting back, we have:
\[ \frac{1}{\frac{2^{\frac{4}{5}}}{3^{\frac{4}{5}}}} = \frac{3^{\frac{4}{5}}}{2^{\frac{4}{5}}} \]

### Step 5: Final Result
Thus, the final value of \(\left(\frac{2}{3}\right)^{-\frac{4}{5}}\) is:
\[ \frac{3^{\frac{4}{5}}}{2^{\frac{4}{5}}} \]

### Summary
The value of \(\left(\frac{2}{3}\right)^{-\frac{4}{5}}\) is \(\frac{3^{\frac{4}{5}}}{2^{\frac{4}{5}}}\).

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