We are tasked with simplifying the expression:  
\[
(5x^4y)^3 \times (3xy^5)^2
\]

### Step 1: Apply the power rule
When raising a product to a power, each factor in the product is raised to that power individually. So:

\[
(5x^4y)^3 = 5^3 \cdot (x^4)^3 \cdot y^3 = 125x^{12}y^3
\]

\[
(3xy^5)^2 = 3^2 \cdot x^2 \cdot (y^5)^2 = 9x^2y^{10}
\]

### Step 2: Multiply the results
Now, we multiply the two simplified expressions:

\[
125x^{12}y^3 \times 9x^2y^{10}
\]

Multiply the constants:

\[
125 \times 9 = 1125
\]

For the \(x\)-terms, use the rule \(x^m \times x^n = x^{m+n}\):

\[
x^{12} \times x^2 = x^{14}
\]

For the \(y\)-terms, use the same rule for exponents:

\[
y^3 \times y^{10} = y^{13}
\]

### Final Answer:
\[
1125x^{14}y^{13}
\]

Let me know if you would like more details or have any questions!

Here are some related questions:
1. How do you simplify expressions involving exponents?
2. What is the power of a product rule in exponents?
3. How can you multiply terms with the same base?
4. What are common mistakes when simplifying exponent expressions?
5. How do exponent rules apply in division?

**Tip:** Always simplify each factor individually when raising a product to a power.

Learn how to simplify the expression (5x^4y)^3 * (3xy^5)^2 step-by-step. This example covers key algebraic concepts such as exponentiation and the power of a product rule. Suitable for students in 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