(4x^5y)^3/(2x^7y)^2

Jasonbradley

2 min read

·

Jun 16, 2024

19

Share

Simplifying Algebraic Expressions: (4x^5y)^3/(2x^7y)^2

This article will guide you through simplifying the algebraic expression (4x^5y)^3/(2x^7y)^2. We'll break down each step to understand the process and arrive at the simplified form.

Understanding the Rules

Before we begin, let's refresh our memory on the key rules of exponents:

• Product of Powers: x^m * x^n = x^(m+n)
• Quotient of Powers: x^m / x^n = x^(m-n)
• Power of a Power: (x^m)^n = x^(m*n)
• Power of a Product: (xy)^n = x^n * y^n

Simplifying the Expression

1. Apply the Power of a Power Rule:

   • (4x^5y)^3 = 4^3 * (x^5)^3 * y^3 = 64x^15y^3
   • (2x^7y)^2 = 2^2 * (x^7)^2 * y^2 = 4x^14y^2

2. Rewrite the Expression:

   • The original expression now becomes: (64x^15y^3) / (4x^14y^2)

3. Apply the Quotient of Powers Rule:

   • (64/4) * (x^15 / x^14) * (y^3 / y^2) = 16x^(15-14)y^(3-2)

4. Simplify the Exponents:

   • 16x^1y^1 = 16xy

Conclusion

Therefore, the simplified form of the expression (4x^5y)^3/(2x^7y)^2 is 16xy. By applying the rules of exponents systematically, we successfully reduced the complex expression to a simpler form.