https://file.aiquickdraw.com/mathbot/file/1729090189562fbgb7g73.jpg

Let's start with problem 16 from the image:

### Problem 16:
Find the value of:

\[
\frac{4}{216^{\frac{2}{3}}} + \frac{1}{256^{-\frac{3}{4}}} + \frac{2}{243^{-\frac{1}{5}}}
\]

### Step-by-Step Solution:

1. **Evaluate \( 216^{\frac{2}{3}} \):**
   \[
   216 = 6^3 \quad \Rightarrow \quad 216^{\frac{2}{3}} = (6^3)^{\frac{2}{3}} = 6^2 = 36
   \]
   So, \( \frac{4}{216^{\frac{2}{3}}} = \frac{4}{36} = \frac{1}{9} \).

2. **Evaluate \( 256^{-\frac{3}{4}} \):**
   \[
   256 = 2^8 \quad \Rightarrow \quad 256^{-\frac{3}{4}} = (2^8)^{-\frac{3}{4}} = 2^{-6} = \frac{1}{64}
   \]
   So, \( \frac{1}{256^{-\frac{3}{4}}} = \frac{1}{\frac{1}{64}} = 64 \).

3. **Evaluate \( 243^{-\frac{1}{5}} \):**
   \[
   243 = 3^5 \quad \Rightarrow \quad 243^{-\frac{1}{5}} = (3^5)^{-\frac{1}{5}} = 3^{-1} = \frac{1}{3}
   \]
   So, \( \frac{2}{243^{-\frac{1}{5}}} = \frac{2}{\frac{1}{3}} = 6 \).

4. **Add the results:**
   \[
   \frac{1}{9} + 64 + 6
   \]

   First, convert \( \frac{1}{9} \) to a decimal or add it directly:
   \[
   \frac{1}{9} + 64 + 6 = 0.1111 + 64 + 6 = 70.1111
   \]

### Final Answer:
\[
70.1111 \quad \text{or} \quad \frac{631}{9}
\]

---

Let me know if you'd like more details or have any questions. Here are 5 related problems for practice:

1. Simplify \( 125^{\frac{2}{3}} + 16^{\frac{3}{4}} \).
2. Evaluate \( \frac{9}{27^{\frac{1}{3}}} + \frac{16}{81^{-\frac{1}{4}}} \).
3. Find the value of \( \frac{8}{512^{\frac{1}{3}}} + \frac{5}{1024^{\frac{1}{5}}} \).
4. Simplify \( \frac{3}{64^{\frac{1}{2}}} + \frac{4}{81^{-\frac{1}{4}}} \).
5. Compute \( 343^{\frac{2}{3}} + 729^{\frac{1}{3}} \).

### Tip:
When dealing with fractional exponents, remember that \( a^{\frac{

Find the value of: (4 / 216^(2/3)) + (1 / 256^(-3/4)) + (2 / 243^(-1/5))

Learn how to simplify a complex expression involving fractional exponents: (4 / 216^(2/3)) + (1 / 256^(-3/4)) + (2 / 243^(-1/5)). This detailed solution covers exponentiation rules, radicals, and simplification methods. Suitable for high school students in grades 10-12.

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