%5E3.jpeg "(2x^-1)^3")
Simplifying (2x^-1)^3
This expression involves several concepts in algebra, including exponents, negative exponents, and the power of a product rule. Let's break it down step by step.
Understanding the Components
- (2x^-1): This is a product of two terms: 2 and x^-1.
- ^3: This indicates that the entire expression (2x^-1) is raised to the power of 3.
Applying the Rules
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Power of a Product Rule: When raising a product to a power, we raise each factor to that power. So, (2x^-1)^3 = 2^3 * (x^-1)^3
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Power of a Power Rule: When raising a power to another power, we multiply the exponents. Therefore, (x^-1)^3 = x^(-1*3) = x^-3
Simplifying the Expression
Putting it all together, we get:
(2x^-1)^3 = 2^3 * x^-3 = 8 * x^-3
Negative Exponent
Remember that a negative exponent indicates the reciprocal of the base raised to the positive version of that exponent. Therefore:
x^-3 = 1/x^3
Final Result
Therefore, the simplified form of (2x^-1)^3 is:
(2x^-1)^3 = 8/x^3