(2x^8)(3x^-1)^2 Simplified

Jasonbradley

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Jun 16, 2024

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Simplifying the Expression: (2x⁸)(3x⁻¹)²

This article will guide you through the process of simplifying the expression (2x⁸)(3x⁻¹)².

Understanding the Rules

Before we begin, let's recall the following rules of exponents:

• Product of powers: xᵃ * xᵇ = xᵃ⁺ᵇ
• Power of a product: (xy)ᵃ = xᵃ * yᵃ
• Power of a power: (xᵃ)ᵇ = xᵃ*ᵇ

Simplifying the Expression

1. Simplify the second term: (3x⁻¹)² = 3² * (x⁻¹)² = 9 * x⁻²

2. Rewrite the expression: (2x⁸)(9x⁻²)

3. Multiply the coefficients: 2 * 9 = 18

4. Combine the x terms using the product of powers rule: x⁸ * x⁻² = x⁸⁻² = x⁶

5. Final simplified expression: 18x⁶

Conclusion

Therefore, the simplified expression of (2x⁸)(3x⁻¹)² is 18x⁶. By applying the rules of exponents, we can efficiently manipulate and simplify expressions involving powers.