https://file.aiquickdraw.com/mathbot/file/1726600047589g7s1xn39.jpg

To simplify \((5x^3y^2)^3\), we need to apply the power of a product rule, which states \((ab)^n = a^n \cdot b^n\). We will distribute the exponent \(3\) to each factor inside the parentheses:

\[
(5x^3y^2)^3 = 5^3 \cdot (x^3)^3 \cdot (y^2)^3
\]

Now simplify each term:

- \(5^3 = 125\)
- \((x^3)^3 = x^{3 \cdot 3} = x^9\)
- \((y^2)^3 = y^{2 \cdot 3} = y^6\)

Thus, the simplified expression is:

\[
125x^9y^6
\]

Would you like more details or have any questions?

Here are 5 related questions to expand on this:

1. How do you simplify expressions with multiple variables raised to powers?
2. What is the general rule for raising powers to another power?
3. How would you handle negative exponents in similar expressions?
4. Can this expression be factored further, or is it in its simplest form?
5. How does the simplification change if there were fractional exponents involved?

**Tip**: When simplifying expressions with exponents, always apply the exponent to every term inside the parentheses!

Learn how to simplify the algebraic expression (5x^3 y^2)^3 using the power of a product rule. This guide walks through key exponent rules and algebraic concepts suitable for Grades 8-10.

Math Problem Statement

Solution

Ask a new question for Free

By Image

Math Problem Analysis

Mathematical Concepts

Formulas

Theorems

Suitable Grade Level

Related Recommendation