https://file.aiquickdraw.com/mathbot/file/1725717866948s0sofqg4.jpg

Let's break down the equation in the image and solve it step by step.

The given equation is:

\[
\left(\frac{1}{2}\right)^{2x - 5} = \sqrt{\frac{16}{2^{2 - x}}}
\]

We need to solve for \( x \), where \( x = p \), and then find the value of \( 5p \).

### Step-by-step solution:

1. **Start with the left-hand side**: 
   \[
   \left(\frac{1}{2}\right)^{2x - 5} = 2^{-(2x - 5)}
   \]
   This is just rewriting the left-hand side using properties of exponents.

2. **Simplify the right-hand side**: 
   \[
   \sqrt{\frac{16}{2^{2 - x}}} = \frac{\sqrt{16}}{\sqrt{2^{2 - x}}} = \frac{4}{2^{(2 - x)/2}}
   \]

3. **Set the two sides equal**:
   \[
   2^{-(2x - 5)} = \frac{4}{2^{(2 - x)/2}}
   \]
   Now, express 4 as \( 2^2 \):
   \[
   2^{-(2x - 5)} = \frac{2^2}{2^{(2 - x)/2}} = 2^{2 - (2 - x)/2}
   \]

4. **Simplify the exponents**:
   \[
   2^{-(2x - 5)} = 2^{2 - \frac{2 - x}{2}}
   \]
   Since the bases are the same, we can equate the exponents:
   \[
   -(2x - 5) = 2 - \frac{2 - x}{2}
   \]

5. **Solve the equation**:
   Multiply both sides by 2 to eliminate the fraction:
   \[
   -2(2x - 5) = 4 - (2 - x)
   \]
   Expand both sides:
   \[
   -4x + 10 = 4 - 2 + x
   \]
   Simplify:
   \[
   -4x + 10 = 2 + x
   \]
   Move all terms involving \( x \) to one side:
   \[
   10 - 2 = 4x + x
   \]
   \[
   8 = 5x
   \]
   \[
   x = \frac{8}{5}
   \]

6. **Find \( 5p \)**:
   Since \( x = p \), we have \( p = \frac{8}{5} \). Therefore, 
   \[
   5p = 5 \times \frac{8}{5} = 8
   \]

Thus, the value of \( 5p \) is **8**.

Would you like more details on any step? Here are a few related questions for practice:

1. What are the properties of exponents used in the solution?
2. How do you simplify expressions involving square roots and fractions?
3. How do you handle equations where the base of the exponents is the same?
4. What happens when you multiply both sides of an equation by a factor?
5. How can you check if the value of \( x \) is correct?

**Tip**: When solving exponential equations, always check if you can rewrite both sides with the same base—it simplifies the process significantly!

Nilai x yang memenuhi persamaan: (1/2)^(2x - 5) = sqrt(16 / 2^(2 - x)) adalah x = p, maka nilai dari 5p = ....

Learn how to solve the exponential equation (1/2)^(2x - 5) = sqrt(16 / 2^(2 - x)) step-by-step. This solution involves key algebraic concepts such as the properties of exponents and simplifying square roots. Suitable for high school students in Grades 10-12.

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