%5E-1.jpeg "(5^-2a^3b^-4)^-1")
Simplifying Expressions with Negative Exponents: (5^-2a^3b^-4)^-1
This article will delve into simplifying the expression (5^-2a^3b^-4)^-1. We'll explore the rules of exponents and how to apply them to solve this problem.
Understanding Negative Exponents
A negative exponent indicates the reciprocal of the base raised to the positive value of the exponent. For example:
- x^-n = 1/x^n
Simplifying the Expression
Let's break down the simplification step by step:
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Apply the power of a power rule: This rule states that (x^m)^n = x^(m*n). Applying this to our expression:
(5^-2a^3b^-4)^-1 = 5^(-2-1)a^(3-1)b^(-4*-1)**
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Simplify the exponents:
5^2a^-3b^4
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Apply the rule for negative exponents:
5^2 * (1/a^3) * b^4
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Simplify the expression:
(25 * b^4) / a^3
Final Result
Therefore, the simplified form of (5^-2a^3b^-4)^-1 is (25b^4)/a^3.
Remember, understanding the rules of exponents is crucial for simplifying expressions with negative exponents. By applying these rules correctly, you can navigate complex expressions and obtain accurate results.