Evaluate each of the following :
`(i)(sqrt(9))^(-3)" "(ii)(3sqrt(8))^(-2)`

Explanation

Let's evaluate the expressions step by step.

### (i) Evaluate \((\sqrt{9})^{-3}\)

**Step 1:** Find the value of \(\sqrt{9}\).
- The square root of 9 is 3.

\[ \sqrt{9} = 3 \]

**Step 2:** Substitute the value back into the expression.
- We replace \(\sqrt{9}\) with 3 in the expression.

\[ (\sqrt{9})^{-3} = (3)^{-3} \]

**Step 3:** Apply the negative exponent rule.
- The negative exponent indicates that we take the reciprocal.

\[ (3)^{-3} = \frac{1}{3^3} \]

**Step 4:** Calculate \(3^3\).
- \(3^3 = 3 \times 3 \times 3 = 27\).

\[ \frac{1}{3^3} = \frac{1}{27} \]

**Final Result for (i):**
\[ (\sqrt{9})^{-3} = \frac{1}{27} \]

---

### (ii) Evaluate \((3\sqrt{8})^{-2}\)

**Step 1:** Rewrite the expression with the negative exponent.
- The negative exponent indicates that we take the reciprocal.

\[ (3\sqrt{8})^{-2} = \frac{1}{(3\sqrt{8})^2} \]

**Step 2:** Square both parts of the expression.
- We can square the 3 and the \(\sqrt{8}\) separately.

\[ (3\sqrt{8})^2 = 3^2 \times (\sqrt{8})^2 \]

**Step 3:** Calculate \(3^2\) and \((\sqrt{8})^2\).
- \(3^2 = 9\)
- \((\sqrt{8})^2 = 8\)

\[ (3\sqrt{8})^2 = 9 \times 8 \]

**Step 4:** Multiply the results.
- \(9 \times 8 = 72\).

\[ (3\sqrt{8})^2 = 72 \]

**Step 5:** Substitute back into the expression.
- Now we can write the expression as:

\[ (3\sqrt{8})^{-2} = \frac{1}{72} \]

**Final Result for (ii):**
\[ (3\sqrt{8})^{-2} = \frac{1}{72} \]

---

### Summary of Results:
1. \((\sqrt{9})^{-3} = \frac{1}{27}\)
2. \((3\sqrt{8})^{-2} = \frac{1}{72}\)

---