(-3x^2y^5)^2

Jasonbradley

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Jun 16, 2024

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Simplifying (-3x^2y^5)^2

In mathematics, simplifying expressions is a fundamental skill. Let's break down how to simplify the expression (-3x^2y^5)^2.

Understanding the Rules

• Exponents: An exponent indicates how many times a base is multiplied by itself. For example, x^2 means x * x.
• Product of Powers: When multiplying powers with the same base, you add the exponents. For example, x^2 * x^3 = x^(2+3) = x^5.
• Power of a Power: When raising a power to another exponent, you multiply the exponents. For example, (x^2)^3 = x^(2*3) = x^6.
• Power of a Product: When raising a product to an exponent, you raise each factor to that exponent. For example, (xy)^2 = x^2 * y^2.

Simplifying the Expression

1. Apply the Power of a Power Rule: We have a power raised to another exponent: (-3x^2y^5)^2. We multiply the exponents inside the parentheses by the exponent outside: (-3x^2y^5)^2 = (-3)^2 * (x^2)^2 * (y^5)^2

2. Simplify each term:

   • (-3)^2 = 9
   • (x^2)^2 = x^(2*2) = x^4
   • (y^5)^2 = y^(5*2) = y^10

3. Combine the terms: 9 * x^4 * y^10 = 9x^4y^10

Conclusion

Therefore, the simplified form of (-3x^2y^5)^2 is 9x^4y^10. By applying the rules of exponents, we have successfully simplified the expression.