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Simplifying Algebraic Expressions
This article will guide you through the simplification of the algebraic expression:
(2x³z²)³/x³y⁴z² * x⁻⁴z³
Step 1: Simplifying the Cube
Begin by simplifying the cube in the numerator:
(2x³z²)³ = 2³ * (x³ )³ * (z²)³ = 8x⁹z⁶
Step 2: Combining Terms
Now, rewrite the entire expression with the simplified cube:
8x⁹z⁶ / x³y⁴z² * x⁻⁴z³
Step 3: Applying Exponent Rules
Recall the following exponent rules:
- xᵃ / xᵇ = xᵃ⁻ᵇ
- xᵃ * xᵇ = xᵃ⁺ᵇ
- x⁻ᵃ = 1 / xᵃ
Applying these rules, we can simplify the expression further:
- 8x⁹⁻³⁺⁻⁴z⁶⁻²⁺³ / y⁴ = 8x²z⁷ / y⁴
Final Result
The simplified form of the expression is 8x²z⁷ / y⁴.
Key Takeaways
This problem demonstrates the importance of understanding basic exponent rules for simplifying algebraic expressions. By systematically applying these rules, we can break down complex expressions into simpler forms.