%5E2.jpeg "(-2x^3y^4)^2")
Simplifying (-2x^3y^4)^2
In mathematics, simplifying expressions is a crucial skill. Let's explore how to simplify the expression (-2x^3y^4)^2.
Understanding the Rules
To simplify this expression, we need to utilize the following rules of exponents:
- Product of powers: (a^m)^n = a^(m*n)
- Power of a product: (ab)^n = a^n * b^n
Applying the Rules
-
Apply the power of a product rule: (-2x^3y^4)^2 = (-2)^2 * (x^3)^2 * (y^4)^2
-
Apply the product of powers rule: (-2)^2 * (x^3)^2 * (y^4)^2 = 4 * x^(32) * y^(42)
-
Simplify the exponents: 4 * x^(32) * y^(42) = 4x^6y^8
Conclusion
Therefore, the simplified form of (-2x^3y^4)^2 is 4x^6y^8.