%5E-3%2F5a%5E2b%5E4.jpeg "(2a^-2b)^-3/5a^2b^4")
Simplifying the Expression: (2a^-2b)^-3/5a^2b^4
This article will guide you through the process of simplifying the given expression: (2a^-2b)^-3/5a^2b^4.
Understanding the Rules
Before diving into the simplification, let's recall some important 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
Step-by-Step Simplification
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Simplify the power of a power: (2a^-2b)^-3 = 2^-3 * a^6 * b^-3
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Apply the negative exponent rule: 2^-3 = 1/2^3 = 1/8
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Combine terms with the same base: (1/8 * a^6 * b^-3) / (5a^2 * b^4) = (1/40) * (a^(6-2)) * (b^(-3-4))
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Simplify the exponents: (1/40) * a^4 * b^-7
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Express the negative exponent in the denominator: (a^4)/(40b^7)
Final Result
Therefore, the simplified form of the given expression (2a^-2b)^-3/5a^2b^4 is (a^4)/(40b^7).