%5E2.jpeg "(-5x^-3y^4)^2")
Simplifying (-5x^-3y^4)^2
This problem involves simplifying an expression with exponents and negative exponents. Here's a step-by-step explanation:
Understanding the Rules
- Exponent Rule: (a^m)^n = a^(m*n)
- Negative Exponent Rule: a^-n = 1/a^n
Applying the Rules
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Distribute the exponent: (-5x^-3y^4)^2 = (-5)^2 * (x^-3)^2 * (y^4)^2
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Simplify each term:
- (-5)^2 = 25
- (x^-3)^2 = x^(-3*2) = x^-6
- (y^4)^2 = y^(4*2) = y^8
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Combine the terms: 25 * x^-6 * y^8 = 25y^8/x^6
Final Answer
Therefore, the simplified form of (-5x^-3y^4)^2 is 25y^8/x^6.