(-2x^2y)^2 X (-3xy^3)

Jasonbradley

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Jun 16, 2024

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Simplifying Expressions with Exponents

This article will guide you through simplifying the expression **(-2x²y)² x (-3xy³) **.

Understanding the Properties of Exponents

Before we begin, let's recall some key exponent properties:

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

Simplifying the Expression

1. Simplify (-2x²y)²:

   • Apply the power of a product rule: (-2x²y)² = (-2)²(x²)²(y)² = 4x⁴y²

2. Combine the simplified terms:

   • We now have: 4x⁴y² * (-3xy³)

3. Multiply the coefficients and combine variables:

   • 4 * -3 = -12
   • x⁴ * x = x⁽⁴⁺¹⁾ = x⁵
   • y² * y³ = y⁽²⁺³⁾ = y⁵

4. Final simplified expression:

   • -12x⁵y⁵

Conclusion

Therefore, the simplified form of (-2x²y)² x (-3xy³) is -12x⁵y⁵. By applying the appropriate exponent rules, we can efficiently simplify complex expressions involving variables and exponents.