Questions tagged [exponent]
The exponent tag has no usage guidance.
6 questions
10
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How should I convince a student who thinks they 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:
$$(16)^{\frac{1}{2}}=(16)^{\frac{2}{4}}=((16)^2)^{\frac{1}{4}}=...
- 26.9k
9
votes
5
answers
4k
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Exponents with Negative Base; with or without Parentheses
How can I convincingly and mathematically explain the reason behind difference between $(-1)^2$ and $-1^2$?
I used to add "negation" to the order of operations, in the same row as multiplication and ...
- 237
7
votes
1
answer
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Rational Powers of Negative Numbers on Basic Calculators
Context: I teach at a small liberal arts school in the US. The students of interest in this question are generally in their first year.
In courses like precalculus and calculus I like to use ...
- 2,334
17
votes
11
answers
2k
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Natural occurrences of a to the (b to the c)?
Are there some natural contexts in which a double exponential occurs,
$x$ to the ($y$ to the $z$):
$$
x ^ {(y ^ z)} \;, \textrm{or} \;, a ^ {(b ^ c)} \; \textrm{?}
$$
Of course one can contrive many ...
- 271
6
votes
0
answers
385
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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, ...
- 241
7
votes
1
answer
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views
Searching activities with "Find the error" strategy for learning maths
I read pages of the book "Elementary and Middle School Mathematics: Teaching Developmentally" by
John A. Van de Walle, Late of Virginia Commonwealth University
Karen S. Karp, Johns Hopkins University
...
- 10.9k