%5E3-x-5x%5E4%2F10x%5E7y%5E13.jpeg "(-2x^2y^5)^3 X 5x^4/10x^7y^13")
Simplifying the Expression (-2x^2y^5)^3 x 5x^4/10x^7y^13
This problem involves simplifying a complex algebraic expression. Let's break it down step-by-step:
Step 1: Simplify the Cube
First, we need to simplify the cube of the expression (-2x^2y^5)^3:
- Apply the power of a product rule: (ab)^n = a^n * b^n
- Apply the power of a power rule: (a^m)^n = a^(m*n)
This gives us: (-2x^2y^5)^3 = (-2)^3 * (x^2)^3 * (y^5)^3 = -8x^6y^15
Step 2: Simplify the Multiplication
Now, let's multiply the simplified expression by 5x^4:
-8x^6y^15 * 5x^4 = -40x^10y^15
Step 3: Simplify the Division
Finally, we divide the product by 10x^7y^13:
-40x^10y^15 / 10x^7y^13 = -4x^3y^2
Conclusion
Therefore, the simplified expression for (-2x^2y^5)^3 x 5x^4/10x^7y^13 is -4x^3y^2.