(3x^5y^3)^5/(6x^10y^7)^2

Jasonbradley

2 min read

·

Jun 16, 2024

24

Share

Simplifying the Expression (3x^5y^3)^5 / (6x^10y^7)^2

This article will guide you through simplifying the algebraic expression (3x^5y^3)^5 / (6x^10y^7)^2. We will utilize the properties of exponents to achieve a simplified form.

Breaking Down the Expression

Let's break down the expression step by step:

1. Distribute the exponents:

   • (3x^5y^3)^5: We distribute the exponent 5 to each factor inside the parentheses. This gives us 3^5 * x^(55) * y^(35) = 243x^25y^15.
   • (6x^10y^7)^2: Similarly, we distribute the exponent 2, resulting in 6^2 * x^(102) * y^(72) = 36x^20y^14.

2. Substitute back into the original expression: The original expression now becomes: (243x^25y^15) / (36x^20y^14).

Simplifying Further

Now we can simplify the expression by applying the following properties of exponents:

1. Dividing exponents with the same base: When dividing exponents with the same base, we subtract the powers.
2. Simplifying numerical coefficients: We can simplify the numerical coefficients by dividing them.

Applying these rules, we get:

• x^25 / x^20 = x^(25-20) = x^5
• y^15 / y^14 = y^(15-14) = y^1 = y
• 243 / 36 = 27/4

Final Simplified Expression

Therefore, the simplified form of the expression (3x^5y^3)^5 / (6x^10y^7)^2 is (27/4)x^5y.