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The given expression is:

\[
\frac{15p^7}{(3p^3)^2}
\]

Let's simplify this step by step.

### Step 1: Simplify the denominator
The denominator is \((3p^3)^2\). To simplify this, apply the power of a product rule:

\[
(3p^3)^2 = 3^2 \cdot (p^3)^2 = 9p^6
\]

So, the expression becomes:

\[
\frac{15p^7}{9p^6}
\]

### Step 2: Simplify the fraction
Now simplify the constants and the powers of \(p\):

\[
\frac{15}{9} = \frac{5}{3}
\]

For the powers of \(p\), subtract the exponent in the denominator from the exponent in the numerator:

\[
p^7 / p^6 = p^{7-6} = p^1 = p
\]

### Final Expression:
After simplification, the final expression is:

\[
\frac{5p}{3}
\]

Would you like further details or have any questions?

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Here are 5 related questions for further practice:
1. How would you simplify \(\frac{20p^8}{(4p^2)^3}\)?
2. What is the general rule for simplifying \(\frac{x^m}{x^n}\)?
3. How can you simplify expressions with more complex powers like \(\frac{18p^{12}}{(6p^4)^2}\)?
4. How would you handle an expression where the denominator has a negative exponent, e.g., \(\frac{12x^5}{(2x^{-2})^3}\)?
5. What happens when the numerator and denominator have the same exponent, like \(\frac{p^4}{p^4}\)?

**Tip:** When simplifying expressions involving exponents, remember the quotient rule: \( \frac{a^m}{a^n} = a^{m-n} \), which allows you to subtract exponents directly when the bases are the same.

Learn how to simplify the algebraic expression 15p^7 / (3p^3)^2 step by step. This problem involves exponent rules, such as the power and quotient rules. Suitable for students in Grades 8-10.

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