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

Jasonbradley

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Jun 16, 2024

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Simplifying the Expression (-2x^2y^5)^3 * 5x^4 / 10x^7y^13

This expression involves several algebraic operations including exponents, multiplication, and division. Let's break it down step-by-step to simplify it.

1. Simplify the Cube:

First, we need to simplify the term (-2x^2y^5)^3. Remember that when raising a power to another power, we multiply the exponents:

(-2x^2y^5)^3 = (-2)^3 * (x^2)^3 * (y^5)^3 = -8x^6y^15

2. Combine the Numerator:

Now, let's multiply the simplified term by 5x^4:

-8x^6y^15 * 5x^4 = -40x^10y^15

3. Simplify the Division:

Next, we divide the result by 10x^7y^13. Remember that when dividing powers with the same base, we subtract the exponents:

-40x^10y^15 / 10x^7y^13 = -4x^3y^2

Therefore, the simplified expression is -4x^3y^2.