%5E-2.jpeg "(2x^3y^-3)^-2")
Simplifying the Expression: (2x^3y^-3)^-2
This article will guide you through simplifying the expression (2x^3y^-3)^-2. We will use the rules of exponents to reach a simplified form.
Understanding the Rules of Exponents
Before diving into the simplification, let's recall the relevant rules of exponents:
- Product of powers: x^m * x^n = x^(m+n)
- Quotient of powers: x^m / x^n = x^(m-n)
- Power of a power: (x^m)^n = x^(m*n)
- Negative exponent: x^-n = 1/x^n
Simplifying the Expression
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Distribute the outer exponent: Applying the power of a power rule, we distribute the -2 exponent to each term within the parentheses: (2x^3y^-3)^-2 = 2^-2 * (x^3)^-2 * (y^-3)^-2
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Simplify each term:
- 2^-2 = 1/2^2 = 1/4
- (x^3)^-2 = x^(3*-2) = x^-6
- (y^-3)^-2 = y^(-3*-2) = y^6
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Combine the terms: 1/4 * x^-6 * y^6 = (1/4) * (1/x^6) * y^6 = y^6 / (4x^6)
Final Result
Therefore, the simplified form of (2x^3y^-3)^-2 is y^6 / (4x^6).