(-2x^5y^7)^3+7x^15y^21

Jasonbradley

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Jun 16, 2024

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Simplifying the Expression: (-2x^5y^7)^3 + 7x^15y^21

This article aims to guide you through the process of simplifying the given expression: (-2x^5y^7)^3 + 7x^15y^21. We'll break down the steps involved to arrive at a simplified form.

Understanding the Properties

Before we begin, let's refresh our understanding of a few key properties in algebra:

• Power of a product: (ab)^n = a^n * b^n
• Power of a power: (a^m)^n = a^(m*n)

Simplifying the Expression

1. Distribute the exponent: We begin by applying the power of a product property to the first term: (-2x^5y^7)^3 = (-2)^3 * (x^5)^3 * (y^7)^3

2. Simplify exponents: Applying the power of a power property, we get: (-2)^3 * (x^5)^3 * (y^7)^3 = -8 * x^(53) * y^(73) = -8x^15y^21

3. Combine terms: Now we can combine the simplified first term with the second term: -8x^15y^21 + 7x^15y^21

4. Factor out the common terms: Both terms have the same variables raised to the same powers (x^15y^21), so we can factor this out: x^15y^21 * (-8 + 7)

5. Final simplification: Simplifying the expression in the parentheses, we get: x^15y^21 * (-1) = -x^15y^21

Conclusion

Therefore, the simplified form of the expression (-2x^5y^7)^3 + 7x^15y^21 is -x^15y^21.