%5E-1%2F6b%5E3.jpeg "(2u^-5)^-1/6b^3")
Simplifying the Expression: (2u^-5)^-1/6b^3
This expression involves several exponent rules and can be simplified to a more readable form. Let's break it down step by step:
Understanding the Rules
- Negative Exponent: A term raised to a negative exponent is equal to its reciprocal with a positive exponent. For example, x^-2 = 1/x^2.
- Power of a Power: When raising a power to another power, multiply the exponents. For example, (x^m)^n = x^(m*n).
- Product of Powers: When multiplying terms with the same base, add the exponents. For example, x^m * x^n = x^(m+n).
Simplifying the Expression
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Dealing with the negative exponent inside the parentheses: (2u^-5)^-1/6 = (2/u^5)^-1/6
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Applying the power of a power rule: (2/u^5)^-1/6 = 2^-1/6 / u^(5*-1/6)
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Simplifying the exponents: 2^-1/6 / u^(-5/6)
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Dealing with the negative exponent in the denominator: 2^-1/6 * u^(5/6)
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Combining with the remaining term: 2^-1/6 * u^(5/6) * b^3
Final Simplified Expression: (2^-1/6 * u^(5/6) * b^3)
This expression is now in its simplest form, free of negative exponents and with the terms clearly separated.
Important Note: This expression can be further simplified depending on the specific requirements of the problem. For instance, you might be asked to express the result using radicals or rewrite 2^-1/6 using a radical.