https://r2.erweima.ai/mathbot/image/172591691962850dnsv3k.jpg

The equation in the image shows:

\[
p^{p^p + p} = p^{p^p} \cdot p^{p^p}
\]

This expression involves exponentiation and multiplication of terms. Let's break it down step by step:

### Left-hand side (LHS):
\[
p^{p^p + p}
\]
This represents \( p \) raised to the power of \( p^p + p \).

### Right-hand side (RHS):
\[
p^{p^p} \cdot p^{p^p}
\]
This represents the product of two terms, both equal to \( p^{p^p} \).

### Simplifying the RHS:
Using the property of exponents:
\[
a^m \cdot a^n = a^{m+n}
\]
We can combine the terms on the RHS:
\[
p^{p^p} \cdot p^{p^p} = p^{p^p + p^p} = p^{2p^p}
\]

### Conclusion:
Thus, the equation simplifies to:

\[
p^{p^p + p} = p^{2p^p}
\]

This is true if and only if \( p^p + p = 2p^p \), which simplifies to:

\[
p^p + p = p^p + p^p
\]
\[
p = p^p
\]

This holds when \( p = 1 \), because \( 1^1 = 1 \).

Therefore, the equation holds true when \( p = 1 \).

Would you like more details or have any questions about this solution?

Here are 5 related questions to further explore this topic:
1. How does the property of exponents help simplify equations like this?
2. What other values of \( p \) would make \( p^p = p \) true?
3. How do exponentiation and multiplication relate to each other in algebra?
4. Can the equation hold for any other values of \( p \), or is \( p = 1 \) the only solution?
5. How would this equation change if different exponents were used?

**Tip**: When simplifying exponential expressions, always look for ways to combine like terms using properties of exponents, such as \( a^m \cdot a^n = a^{m+n} \).

The equation p^(p^p + p) = p^(p^p) * p^(p^p) is shown. Simplify and solve.

Learn how to simplify and solve the exponential equation p^(p^p + p) = p^(p^p) * p^(p^p) using properties of exponents. This problem covers advanced algebra concepts and is suitable for students in Grades 10-12.

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