Simplify each of the folloiwing and express with positive index :
`((27^(-3))/(9^(-3)))^((1)/(5))`

Answer

To simplify the expression \(\left(\frac{27^{-3}}{9^{-3}}\right)^{\frac{1}{5}}\), we will follow these steps:

### Step 1: Rewrite the bases in terms of powers of 3
We know that:
- \(27 = 3^3\)
- \(9 = 3^2\)

Thus, we can rewrite the expression as:
\[ \left(\frac{(3^3)^{-3}}{(3^2)^{-3}}\right)^{\frac{1}{5}} \]

### Step 2: Apply the power of a power property
Using the property \((a^m)^n = a^{m \cdot n}\), we can simplify the numerator and denominator:
\[ \left(\frac{3^{3 \cdot -3}}{3^{2 \cdot -3}}\right)^{\frac{1}{5}} = \left(\frac{3^{-9}}{3^{-6}}\right)^{\frac{1}{5}} \]

### Step 3: Simplify the fraction
Using the property \(\frac{a^m}{a^n} = a^{m-n}\), we simplify the fraction:
\[ 3^{-9 - (-6)} = 3^{-9 + 6} = 3^{-3} \]

### Step 4: Apply the outer exponent
Now we apply the outer exponent \(\frac{1}{5}\):
\[ (3^{-3})^{\frac{1}{5}} = 3^{-3 \cdot \frac{1}{5}} = 3^{-\frac{3}{5}} \]

### Step 5: Express with a positive index
To express the result with a positive index, we use the property \(a^{-m} = \frac{1}{a^m}\):
\[ 3^{-\frac{3}{5}} = \frac{1}{3^{\frac{3}{5}}} \]

### Final Answer
Thus, the simplified expression is:
\[ \frac{1}{3^{\frac{3}{5}}} \]

---