Find the limit of $\sqrt[5]{x^5-x^4}-x$ as $x$ approaches $\infty $

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Learn how to solve limits by rationalizing problems step by step online. Find the limit of (x^5-x^4)^(1/5)-x as x approaches infinity. Factor the polynomial x^5-x^4 by it's greatest common factor (GCF): x^{4}. The power of a product is equal to the product of it's factors raised to the same power. Simplify \sqrt[5]{x^{4}} using the power of a power property: \left(a^m\right)^n=a^{m\cdot n}. In the expression, m equals 4 and n equals \frac{1}{5}. Applying rationalisation.