Find the limit of $\left(\frac{\left(4+x\right)^{-1}}{x}\right)^{-1\cdot 4^{-1}}$ as $x$ approaches 0

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$\lim_{x\to0}\left(\left(\frac{1}{x\left(4+x\right)^{1}}\right)^{-1\cdot 4^{-1}}\right)$

Learn how to solve limits by direct substitution problems step by step online. Find the limit of (((4+x)^(-1))/x)^(-4^(-1)) as x approaches 0. Applying the property of exponents, \displaystyle a^{-n}=\frac{1}{a^n}, where n is a number. Any expression to the power of 1 is equal to that same expression. Multiply the single term x by each term of the polynomial \left(4+x\right). When multiplying two powers that have the same base (x), you can add the exponents.