We are given the equation:

\[
2^4 - 3x = 16^{\frac{2}{5}}
\]

### Step 1: Simplify both sides.

#### Left side:
\[
2^4 = 16
\]
So the equation becomes:
\[
16 - 3x = 16^{\frac{2}{5}}
\]

#### Right side:
We know that \( 16 = 2^4 \), so:
\[
16^{\frac{2}{5}} = (2^4)^{\frac{2}{5}} = 2^{\frac{8}{5}}
\]
Thus, the equation is now:
\[
16 - 3x = 2^{\frac{8}{5}}
\]

### Step 2: Solve for \( x \).

We want to isolate \( x \), so first subtract 16 from both sides:
\[
-3x = 2^{\frac{8}{5}} - 16
\]

Now, divide by -3:
\[
x = \frac{16 - 2^{\frac{8}{5}}}{3}
\]

### Final Answer:
The value of \( x \) is:

\[
x = \frac{16 - 2^{\frac{8}{5}}}{3}
\]

Let me know if you'd like a numerical approximation, further explanation, or if you have any other questions!

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### Related Questions:
1. How do you evaluate exponents with fractional powers?
2. What is the process of solving equations involving powers of 2?
3. How do you simplify expressions involving powers of powers?
4. What are common methods to isolate variables in linear equations?
5. What are the general steps to solve equations with exponents?

#### Tip: 
When dealing with fractional exponents, remember that \( a^{\frac{m}{n}} \) is equivalent to \( \sqrt[n]{a^m} \).

Learn how to solve the equation 2^4 - 3x = 16^(2/5) step by step, using the laws of exponents and algebraic manipulation. This solution demonstrates how to handle fractional exponents and simplify both sides of the equation. Suitable for students in Grades 9-11.

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