(-2x^2y^5)^3 X 5x^4/10x^7y^13

2 min read Jun 16, 2024
(-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.

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