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The expression you provided is:

\[
\frac{16^{3/4}}{81^{1/3}}
\]

### Step-by-Step Solution:

1. **Simplify the numerator**: \(16^{3/4}\)

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

2. **Simplify the denominator**: \(81^{1/3}\)

   - \(81 = 3^4\), so:
     \[
     81^{1/3} = (3^4)^{1/3} = 3^{4 \times \frac{1}{3}} = 3^{4/3}
     \]
     We can leave \(3^{4/3}\) in its simplified fractional form or calculate an approximate value.

3. **Combine the results**:

   Now, the expression becomes:
   \[
   \frac{8}{3^{4/3}}
   \]

   This is the simplified form of the given expression.

If you want a numerical value, you can further approximate \(3^{4/3} \approx 4.326\), which gives:
\[
\frac{8}{4.326} \approx 1.849
\]

Thus, the value of the expression is approximately **1.849**.

Would you like more details or have any questions?

### Related Questions:
1. How can you generalize the simplification of fractional exponents?
2. What is the relationship between roots and fractional powers?
3. Can you simplify \( \frac{32^{5/2}}{64^{3/4}} \)?
4. What does it mean for a number to be raised to a fractional power?
5. How would the result change if you used different base numbers?

### Tip:
When simplifying expressions with fractional exponents, remember that the numerator of the exponent represents a power, and the denominator represents a root.

Simplify and find the value of 16^(3/4) / 81^(1/3).

Learn how to simplify and find the value of the expression 16^(3/4) divided by 81^(1/3) using the laws of exponents. This step-by-step guide will walk you through handling fractional powers and exponent rules, suitable for students in Grades 8-10.

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