# Questions tagged [exponent]

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### Rational Powers of Negative Numbers on Basic Calculators

Context: I teach at a small liberal arts school in the US. The students of interest in this question are generally in their first year. In courses like precalculus and calculus I like to use ...
2k views

### Natural occurrences of a to the (b to the c)?

Are there some natural contexts in which a double exponential occurs, $x$ to the ($y$ to the $z$): $$x ^ {(y ^ z)} \;, \textrm{or} \;, a ^ {(b ^ c)} \; \textrm{?}$$ Of course one can contrive many ...
477 views

### How should I convince a student who proved $1=-1$

One of my high school students who has ZERO knowledge on complex numbers and the modulus function has showed me the following algebra: (16)^{\frac{1}{2}}=(16)^{\frac{2}{4}}=((16)^2)^{\frac{1}{4}}=...
371 views

### What books properly address the properties of $a^b$?

Many students think $\sqrt{a} \sqrt{b}=\sqrt{a\ b}$ $\sqrt{a^2}=a$ $\frac{1}{\sqrt{a}}=\sqrt{\frac{1}{a}}$ but none of the above are true when (a) and (b) are negative. To avoid such problems, ...
How can I convincingly and mathematically explain the reason behind difference between $(-1)^2$ and $-1^2$? I used to add "negation" to the order of operations, in the same row as multiplication and ...