%5E2.jpeg "(5x^2y^3)^2")
Simplifying (5x²y³)²
This article will guide you through simplifying the expression (5x²y³)².
Understanding Exponents
An exponent indicates how many times a base number is multiplied by itself. In this case, the base is **(5x²y³) ** and the exponent is 2.
Applying the Power of a Product Rule
The power of a product rule states that **(ab)**ⁿ = aⁿbⁿ. We can apply this rule to our expression:
(5x²y³)² = 5² (x²)² (y³)²
Simplifying the Expression
Let's simplify each term:
- 5² = 25
- (x²)² = x⁴ (Applying the power of a power rule: (aⁿ)ᵐ = aⁿᵐ)
- (y³)² = y⁶ (Applying the power of a power rule)
Now, combining the simplified terms:
25x⁴y⁶
Conclusion
Therefore, the simplified form of (5x²y³)² is 25x⁴y⁶.