Mathematics Stack Exchange
Mathematics Stack Exchange

Questions tagged [exponentiation]

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

Exponentiation is a mathematical operation which produces a power $a^n$ from a base $a$ and an exponent $n$. The objects involved are usually numbers, but the procedure can be generalized to matrices, elements in algebraic structures, sets, etc.

4326 questions
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simplification of squared expression

I haven't done a math class in a while and I'm stumped on what seems to be a simple question. How does $$ ( [(k + 1)^2]/4 ) (k + 2)^2$$ simplify to $$ [ (k + 1)(k + 2)/2 ]^2 $$ What rule of simplifying exponents applies to this?
jsan
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Pandigital exponent solution?

I don't have Reviewing C++ By Alex Maurea book. But someone in facebook post a question from this book which is following You can see the puzzle at page 542 problem 29. Now I think the answer should be log2123456798. Am I right or I am tackling the…
Anirban Nag 'tintinmj'
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exponent manipulation - $4^{21} \cdot 5^{11} = 2 \cdot 10^{n}$ - what is $n$?

I was taking a practice GMAT test and it had a question like this: $4^{21} \cdot 5^{11} = 2 \cdot 10^n$ What is $n$? The available answers were something like 16 22 23 24 32 I'm not exactly sure on the multiple choice options... However I'm not…
kralco626
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Complicated rational exponents

How is this $\frac{m}{n}$ equals to $m \times \frac{1}{n}$? Any logical proof for this? Which draws this conclusion: A fractional exponent like $\frac{m}{n}$ means do the $m^{\text{th}}$ power, then take the $n^{\text{th}}$ root or take the…
user962206
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Unary minus on squared number

According to algebra as I know it, $-2^2 = 4$, but most calculators expand this to $-2 * 2 = -4$, which yields a different answer. This is because of the order of precedence. In traditional math, I've seen that the unary operator is applied before…
kettlecrab
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Equation with a division in exponent

I have an equation: 10,9 * 2^(x/1,5) = 1000 and want to calculate the value of x. x being in the exponent is my problem. How can I get to something like: x = ...
Christoph
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x raised by the power of y equals infinity.

How many zeros are there in this equation? 10000^999 In my calculator it says infinity but that doesn't seem right.
Rockyfelle
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Method to solve this type of equation

It seems simple yet I have to show how I got to the answer... I've been Googling, but can't narrow it down. $8 = 2^x$ Thanks in advance.
sparecycle
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Simplifying euler exponent?

How would I go about simplifying and finding the exact value for this question: $e^{6\ln(4)}$ I know that $e ^{\ln x} = x$ but how does the $6$ affect this answer?
user1804933
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Simplify the expression.

Simplify the following expressions using fractional exponents, I forgot how to do this type, do I rationalize it? or can it just cancel each other out? $ {\Large \frac{\sqrt[ 5 ]{x^{ 3 }}}{ \sqrt{x} } = }$ ? Cheers
user95012
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What's the pattern? roots and powers of n?

I won't hold it against anyone if this is considered a bad question but I just don't know how else to put it and really want to know. 1st case: n = positive integer a = $\sqrt n$ b = 1 2nd case: n = positive integer a = $b^2$ b = $\sqrt[3]n$ c =…
RussW
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How to manually compare two different powers of any two different natural numbers (is there a universal algorithm)?

The ability of manually comparing any powers of any natural numbers is one of my greatest dreams. "Manually" means without a calculator, or a computer, or any other device besides my own head and possibly also a pencil and paper. For example, we…
Alexander
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Power Law Decay

I have the following data: \begin{array}{|c|c|} \hline t & KE \\ \hline 0 & 3.250 \\ \hline 0.0000416 & 1.505 \\ \hline 0.0000832&0.526 \\ \hline 0.000125 & 0 \\ \hline 0.000166 & 0 \\ \hline 0.000208 & 0 \\ \hline 0.000250 & 0 \\…
rdemo
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Does the value of $(-37)^{1/33}$ exist?

Does the value of $(-37)^{1/33}$ exist? I am very much confused with this. In desmos it is giving a real value whereas on the other hand in Wolfram Alpha it is giving an imaginary value. So, please give me the right answer? I want to know who is…
Kartik Ghosh
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Simplifying fractional exponents with variables

The problem I do not understand how the exponents are simplified to $\frac pq-1$ in the expression in the image
user1230116
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