%5E3-without-negative-exponents.jpeg "(2x^-1)^3 Without Negative Exponents")
Simplifying (2x^-1)^3 without Negative Exponents
This expression involves both a negative exponent and a power of a power. Let's break it down step-by-step to get rid of the negative exponent:
Understanding the Properties
- Negative Exponents: A negative exponent indicates the reciprocal of the base raised to the positive version of the exponent. For example, x^-1 = 1/x.
- Power of a Power: When raising a power to another power, you multiply the exponents. For example, (x^m)^n = x^(m*n).
Applying the Properties to our Expression
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Addressing the Negative Exponent: (2x^-1)^3 = (2 * (1/x))^3
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Simplifying Inside the Parentheses: (2 * (1/x))^3 = (2/x)^3
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Applying the Power of a Power Rule: (2/x)^3 = 2^3 / x^3
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Evaluating the Constant: 2^3 / x^3 = 8/x^3
Final Result
Therefore, (2x^-1)^3 simplified without negative exponents is 8/x^3.