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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Simplifying exponents

I've been refreshing my maths over the last couple of weeks, and it's been a challenge since it has been a long time since I was actively using it (20+ years). Anyways, Khan Academy and old textbooks have been a lot of help, but I am stuck on a few…
MathAgain
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Domains closed under exponentiation

Apart from $\mathbb{N}$ and $\mathbb{C}$, which other domains satisfy $\forall x, y \in D, x^y \in D$ ,i.e. are closed under exponentiation?
A Moshbear
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How to solve $0.5^{1200}\times (2^{1204})$?

I've been struggling with this one. I know that the anwser is $16$, but how do I solve this on paper? $0.5^{1200}\times 2^{1204}$ I know that this has something to do with first subtracting the "powers of n" from each other, but... Step by step is…
Kasperi Koski
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Solving an equation in $x$, in which $x$ occurs as exponent four times

Find the number of solutions to the equation $$2011^x+2012^x+2013^x-2014^x=0$$ The answer seems to be zero, but I have no idea why. Please avoid considering complex solutions and other scary things.
Shubham
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How to quickly identify perfect powers

In a test I'll take there may be a question such as the following: A perfect power is an integer that can be written as $a^b$, $a$ and $b$ being integers greater or equal to 2. One of the following numbers is not a perfect power, which one is…
mmt
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Do exponential identities not apply for negative numbers?

Recently I had a thought that got me thinking. There is the identity $\left (a^b\right )^c=a^{bc}$. If I now take this identity I can do this:$$(-1)=(-1)^{2\cdot 0.5}=\left ((-1)^2\right )^{0.5}=1^{0.5}=1.$$Isn't an identity supposed to be true for…
tempdev nova
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How to calculate the exponent of a given number.

Here's my problem : I can't figure how to get back my exponent Here the formula I use to get a given number : $$a(\text{const}) = 200,\quad b(\text{const}) = 1.1,\quad c(\text{var}) = 50$$ So $c$ is the parameter I pass to my formula and that I…
alyssaw20
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Basic doubt about exponents.

I have a doubt regarding this: $\begin{aligned} \ln y &=\ln \left(x^{x^{x}}\right) \\ &=x \ln \left(x^{x}\right) \\ &=x \cdot x \cdot \ln x \\ &=x^{2} \cdot \ln x \\ &=\ln \left(x^{x^{2}}\right) \neq \ln \left(x^{x^{x}}\right) \end{aligned}$ I KNOW…
GuyEternal
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Solve $x^{x^{x^{2017}}}=2017$

I have tried to use $\ln$, but couldn't solve: \begin{equation} \ln x^{x^{x^{2017}}}=x^{x^{2017}}\ln x=\ln 2017. \end{equation} I found that $x=\sqrt[2017]{2017}$ is a solution, and it is easy to check it. But how to find that solution without…
Lee
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Interpretation of multi-exponent x^y^z ($x^{y^z}$ or ${x^y}^z$)

Is there any generally accepted or written rule specifying the interpretation of a multi-exponent expression written in this simple style (by user, no latex): x^y^z? It leads to different results on different engines: e.g. 5^2^3 can be interpreted…
dev0experiment
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Exponential Sum - Solve for X

I'm wondering if there is a way to solve for x given the following equation: $$A^x + B^x = C^x$$ where A, B, and C are known constants. For pythagorean triples, $x = 2$. I've seen a lot of stuff for sums of exponents (often using Taylor expansion)…
Matt Dodge
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How can we prove for the solutions of the equation $x^y=y^z=z^a...$?

How can we prove for the solutions of the equation $x^y=y^z=z^a...$? You could natural log all of them and then proceed but I’m kind of confused. How would you solve for the solutions of a simpler case then, for example $x^y=y^z=z^x$? Since I think…
Physics_Learner
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Why does this work? What is the best exponent to approximate the logarithm?

Suppose i want to get a upper bound of $log_53$ without other tools than elementary algebra. I can do this: Let $x = log_53$, then $5^x=3$ I raise both sides to $4$, then: $(5^x)^4 = 3^4$ And since $3^4 < 5^3$ it follows that $5^{4x} < 5^3$, then…
ESCM
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what is the value of $9^{ \frac{a}{b} } + 16^{ \frac{b}{a} }$ if $3^{a} = 4^{b}$

I have tried to solve this expression but I'm stuck: $$9^{ \frac{a}{b} } + 16^{ \frac{b}{a} } = 3^{ \frac{2a}{b} } + 4^{ \frac{2b}{a} }$$ and since $3^{a} = 4^{b}$: $$3^{ \frac{2a}{b} } + 4^{ \frac{2b}{a} } = 4^{ \frac{2b}{b} } + 3^{ \frac{2a}{a} }…
Omar Mohamed Khallaf
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Units in exponent - e.g. solve: $2^{3 years}$

What happens to units in an exponent? My math textbook just introduced the exponential equation: $$A_t = Pe^{rt}$$ I've always made it a point in solving math problems to include the units in every calculation. After I plug in my values: $$A_{9…
Web_Designer
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