# Tagged Questions

Questions about exponentiation, the operation of raising a base $b$ to an exponent $a$ to give $b^a$.

38 views

### Arranging set A and B to maximize their power

Given two sets A and B each with $n$ positive reals. How to arrange elements in A and B such that $$\prod_{i=1}^n a_i^{b_i}$$ is maximized? Will ascending order of A and B make the correct ...
119 views

### $(-32)^{\frac{2}{10}}\neq(-32)^{\frac{1}{5}}$?

Is exponentiation by rational numbers defined only for simple fractions? $(-32)^{\frac{2}{10}}=\sqrt[10]{(-32)^2}=\sqrt[10]{1024}=\pm2$ (and $8$ other complex roots) ...
155 views

### Why is $0^0$ also known as indeterminate? [duplicate]

I've seen on Maths Is Fun that $0^0$ is also know as indeterminate. Seriously, when I wanted to see the value for $0^0$, it just told me it's indeterminate, but when I entered this into the exponent ...
193 views

### $1^x = 1^y$ and $x,y$ belongs to Real Numbers.

$1^x = 1^y$, and $x,y \in \mathbb{R}$. Following the rule, same base has powers equal every $x$ should be equal to every $y$. $$1^x = 1^y$$ $$x = y$$ What went wrong?
51 views

### Is this identity correct?

Is this identity true? Wolfram|Alpha thinks is not. $$x^{ln(x^3)} = e^{3\,[ln(x)]^2}$$ That's how I demonstrated it: $${\left(e^{ln(x)}\right)}^{3\,ln(x)} = e^{3\,[ln(x)]^2}$$ ...