To solve the inequality:

\[
\left(\frac{1}{2}\right)^{5p} > \left(\frac{1}{2}\right)^{4p+3}
\]

### Step-by-step Solution:

1. Since the base of both sides of the inequality is \(\frac{1}{2}\), we can compare the exponents directly. This works because \(\frac{1}{2}\) is between 0 and 1, and for numbers between 0 and 1, the larger the exponent, the smaller the value (and vice versa).

2. The inequality becomes:
   \[
   5p < 4p + 3
   \]
   Notice that the inequality sign flipped because the base \(\frac{1}{2}\) is less than 1.

3. Now, solve for \(p\):
   \[
   5p - 4p < 3
   \]
   \[
   p < 3
   \]

### Final Answer:
The solution to the inequality is:
\[
p < 3
\]

Would you like more details or have any questions?

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Here are 5 related questions to explore further:
1. What happens if the base of the inequality was greater than 1?
2. Can you solve a similar inequality with other bases, like \(3^p > 3^{p+2}\)?
3. How does the inequality change if the exponents contain more terms?
4. How would the solution change if the inequality were \(\leq\) instead of \(>\)?
5. How would you solve \(5^p > 5^{2p-1}\)?

**Tip:** When dealing with inequalities involving powers of the same base, always pay attention to the value of the base to decide whether to reverse the inequality sign.

Learn how to solve the exponential inequality (1/2)^5p > (1/2)^(4p+3) with a detailed step-by-step solution. This problem explores key concepts in exponential inequalities, exponent laws, and how to handle inequalities with bases between 0 and 1. Suitable for students in Grades 9-12.

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