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The question asks you to simplify the following expression:

\[
(16)^{-3/4} + 2^{-3} + (8)^{-2/3}
\]

Let's simplify each term one by one:

### Step 1: Simplify \( (16)^{-3/4} \)
We know that \( 16 = 2^4 \). So,

\[
(16)^{-3/4} = (2^4)^{-3/4} = 2^{4 \times (-3/4)} = 2^{-3} = \frac{1}{2^3} = \frac{1}{8}
\]

### Step 2: Simplify \( 2^{-3} \)
This is straightforward:

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

### Step 3: Simplify \( (8)^{-2/3} \)
We know that \( 8 = 2^3 \). So,

\[
(8)^{-2/3} = (2^3)^{-2/3} = 2^{3 \times (-2/3)} = 2^{-2} = \frac{1}{2^2} = \frac{1}{4}
\]

### Step 4: Add all the simplified terms
Now, adding all the terms:

\[
\frac{1}{8} + \frac{1}{8} + \frac{1}{4}
\]

To add these fractions, we need a common denominator. The least common denominator is 8. So,

\[
\frac{1}{4} = \frac{2}{8}
\]

Now add the fractions:

\[
\frac{1}{8} + \frac{1}{8} + \frac{2}{8} = \frac{4}{8} = \frac{1}{2}
\]

Thus, the expression simplifies to \( \frac{1}{2} \).

### Final Answer:
The answer is:

\[
\boxed{\frac{1}{2}}
\]

Would you like more details or clarification? Here are five related questions for further exploration:

1. How do fractional exponents relate to radicals?
2. What are the steps to convert negative exponents into positive exponents?
3. How can we quickly find the least common denominator when adding fractions?
4. Why does \( 16^{-\frac{3}{4}} \) convert to \( 2^{-3} \)?
5. Can these exponent rules be extended to more complex algebraic expressions?

**Tip:** When working with exponents, always try to express numbers as powers of smaller primes like 2 or 3 for easier simplification.

(16)^(-3/4) + 2^(-3) + (8)^(-2/3) is equivalent to?

This math problem demonstrates how to simplify expressions involving fractional exponents. The key concepts covered include exponent rules and finding the least common denominator. Suitable for students in Grades 9-11.

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