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

2 min read Jun 16, 2024
(3x^4y^3)^2 Simplified

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

This article will walk you through simplifying the expression (3x^4y^3)^2. We will break down each step and explain the concepts involved.

Understanding the Expression

The expression (3x^4y^3)^2 represents the square of a monomial.

  • Monomial: A monomial is a single term algebraic expression.
  • Square: Squaring a number or an expression means multiplying it by itself.

Applying the Rules of Exponents

To simplify this expression, we need to apply the following rules of exponents:

  • Power of a product: (ab)^n = a^n * b^n
  • Power of a power: (a^m)^n = a^(m*n)

Step-by-Step Solution

  1. Apply the power of a product rule:

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

  2. Apply the power of a power rule:

    3^2 * (x^4)^2 * (y^3)^2 = 9 * x^(42) * y^(32)

  3. Simplify:

    9 * x^(42) * y^(32) = 9x^8y^6

Conclusion

Therefore, the simplified form of (3x^4y^3)^2 is 9x^8y^6.

This process demonstrates how to effectively simplify expressions involving exponents and monomials by applying the rules of exponents.

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