(3x^4y)(2y^2)^3

Jasonbradley

less than a minute read

·

Jun 16, 2024

15

Share

Simplifying Expressions: (3x^4y)(2y^2)^3

This article explores the process of simplifying the expression (3x^4y)(2y^2)^3.

Understanding the Exponent Rules

To simplify this expression, we'll utilize the following exponent rules:

• Product of powers: x^m * x^n = x^(m+n)
• Power of a product: (xy)^n = x^n * y^n
• Power of a power: (x^m)^n = x^(m*n)

Step-by-Step Simplification

1. Simplify the exponent: (2y^2)^3 = 2^3 * (y^2)^3 = 8y^6

2. Rewrite the expression: (3x^4y)(8y^6)

3. Multiply the coefficients: 24x^4y^7

Final Result

The simplified form of the expression (3x^4y)(2y^2)^3 is 24x^4y^7.

Conclusion

By applying the fundamental exponent rules, we effectively simplified the given expression. This process highlights the importance of understanding exponent properties for manipulating and simplifying algebraic expressions.