Why is $a^{-x}$ defined to be equal to $\frac{1}{a^x}$?
103223
If $x^a$ is $x$ multiplied $a$ times, then how does $x^{-1}$ make sense?
34762
Why isn't $\int \frac{1}{x}~dx = \frac{x^0}{0}$?
100968
Why is $|e^{i \lambda z}| |e^{- \lambda y}|= |e^{- \lambda y}|$ here?
108633
Why $f^{-1}(f(A)) \not= A$
152326
What is the inverse of the function $x \mapsto \frac{ax}{\sqrt{a^2 - |x|^2}}$?
41645
Checking my understanding: $1 - 1 + 1 - 1 + 1 - ... = \frac{1}{2}$
17542
Why is $\sqrt{-x}*\sqrt{-x}=-x?$
130854
Constructing example showing $\mathbb{E}(X^{-1})=(\mathbb{E}(X))^{-1}$
60261
Is $\sqrt{x^2}=|x|$ or $=x$? Isn't $(x^2)^\frac12=x?$
68746
What is $f(f^{-1}(A))$?
133614
Why is $x^{\log_x n}=n$?
151109
Verification that $\lim_{x \to a}\frac{f(x)-f(a)}{x-a}$ and $\lim_{h\to 0}\frac{f(a+h) -f(a)}{h}$ are equivalent definitions of the derivative.
107390
Why is (-1)(-1) = 1?
43430
What exactly does $\frac{dx}{dy}$ mean?
142725
The general solution of $x^a = a^x$ for real $a >0$
59818
Why $(-2)^{2.5}$ isn't equal to $((-2)^{25})^{1/10}$?
43226
Intuition behind logarithm inequality: $1 - \frac1x \leq \log x \leq x-1$