Find the GCF of the following expressions. (Assume x and y are integers and that n is nonzero.)
2x6ny7n, 10x9ny6n

To find the Greatest Common Factor (GCF) of the expressions \( 2x^{6n}y^{7n} \) and \( 10x^{9n}y^{6n} \), follow these steps:

### Step 1: Identify the GCF of the numerical coefficients.
- The numerical coefficients are 2 and 10.
- The GCF of 2 and 10 is 2.

### Step 2: Identify the GCF of the variables \(x\) with their respective exponents.
- The exponents of \(x\) in the two expressions are \(6n\) and \(9n\).
- The GCF of these exponents is the smallest exponent, which is \(6n\).

### Step 3: Identify the GCF of the variables \(y\) with their respective exponents.
- The exponents of \(y\) in the two expressions are \(7n\) and \(6n\).
- The GCF of these exponents is the smallest exponent, which is \(6n\).

### Step 4: Combine the GCFs from each part.
- The GCF of the entire expression is \(2x^{6n}y^{6n}\).

### Final Answer:
\[
\text{GCF} = 2x^{6n}y^{6n}
\]

Would you like more details or have any questions?

---

Here are 5 related questions you might find interesting:

1. How do you find the GCF of more than two algebraic expressions?
2. What is the Least Common Multiple (LCM) of \(2x^{6n}y^{7n}\) and \(10x^{9n}y^{6n}\)?
3. How would you find the GCF if the exponents were negative?
4. Can the GCF of two expressions ever be 1?
5. How does the GCF relate to simplifying fractions in algebra?

**Tip:** When finding the GCF of algebraic expressions, always focus on the smallest power of each variable involved.

Learn how to find the Greatest Common Factor (GCF) of the algebraic expressions 2x^6ny^7n and 10x^9ny^6n with a step-by-step solution. This problem covers key algebraic concepts, including polynomials, exponents, and GCF. Suitable for students in Grades 7-9.

Math Problem Statement

Solution

Ask a new question for Free

By Image

Math Problem Analysis

Mathematical Concepts

Formulas

Theorems

Suitable Grade Level

Related Recommendation