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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Solving $KL^{2C} - LC^{2C} = (B-C)C^{2C} - C^{2C}(T+KG^2) - KP^2$ for $L$

How can I solve this equation for $L$. Everything else is known number: $$KL^{2C} - LC^{2C} = (B-C)C^{2C} - C^{2C}(T+KG^2) - KP^2$$
Николай Караджов
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Instead of $x^{4/3}$ do $(x^4)^{1/3}$

I'm doing a little filter processing research and at one point I expand a signal by applying: $x^{4/3}$ to the signal which will only yield real outputs for real, positive inputs. Since $(x^a)^b = (x^b)^a $ and $(x^a)^b = x^{a \cdot b}$ I asked…
Alon
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$x^2 * (x+1)^2 = (x^2+x)^2$|| I do not understand this

$$x^4(x+1)^4(2x+1)$$ I was solving this question (I had integrate it) but I did not know how to solve it! So I saw the solution and it says $$x^4(x+1)^4 = (x^2+x)^4$$ and I do not get how that works? Can someone prove it, please?
hiyum
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Rational exponent question

Do all rational exponents have whole number base integer derived from the fraction? $a^b=c$ where $a$ and $c$ are whole numbers and $b$ is fraction example: $b= 5/4$ How do I get $a$ that gives first whole $c$, please? Thank you in advance for…
user472405
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Products of e to fractional exponents

I'm quite happy dealing with simple exponents, or so I thought. I've come across the following product and solution: $$ e^{-x^2/2\alpha^2}\times e^{-2x^2/\alpha^2}=e^{-5x^2/2\alpha^2} $$ When I work this through, I get the following instead: $$…
discojoe
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what does define $a^x$ for any $a \in \Bbb R$ and $x \in \Bbb Z$ mean?

wikipedia says for positive integer exponents its defined by the initial condition $b^1=b$ and the recurrence relation $b^{n+1} = b^n*b$ and for negative integers its defined as $a^{-n}=\frac{1}{a^n}$. so is this definition of $a^x$ for all…
James Doherty
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How to calculate big exponents (with modular division involved)?

I found the following equation online when working with cryptography. 1702^2732 x 2083^2526 = 704 mod 3119 Now I'd like to understand the math behind: how do we calculate exponentiation with number that high? how did we get this mod part? From the…
CorellianAle
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Puzzled over basic exponentiation problem with complex argument

I can't figure out where is my erroneous thinking in the following elementary use of exponents. I have used Mathematica to verify that I don't know what I'm doing. $$ a^{bc}=\left(a^{b}\right)^{c} $$ Mathematica says "True". $$…
Oscar
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Without using a calculator how can we say 6^20> 3.10^8?

Please help me understand the method you are using.
Mervin Jacob
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How can I quantify evidence of power law?

I have data from simulations I have run on FORTRAN, and the result looks like a power law relationship when plotting a log-log graph. How can I write this mathematically? I've attached an image. Thanks in advance.Power Law Figure
user309575
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Why can't we cancel the x from both sides in the equation $x^2=x^3$?

It may seem at first sight that the $x$ can be cancelled from both sides. It doesn't make any sense that the square of a number is equal to its cube (unless it's 1) as in this case. I know that the reason of this is pretty well known. Well, as it…
crazypanda666
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Finding $\frac {8}{x^{a-b}+1}+\frac {8}{x^{b-a}+1} = ?$

$$\frac {8}{x^{a-b}+1}+\frac {8}{x^{b-a}+1} = ?$$ My attempt: $$\frac {8}{x^{a-b} + 1} = 8. x^{-a+b}-1 \tag 1$$ $$\frac {8}{x^{b-a} + 1} = 8. x^{a-b}-1 \tag 2$$ I think I've gone too wrong.
Flisch
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When do the index laws stop working?

I've heard before that some index laws don't apply in some situations, like when the base is negative. For example, I entered $y = (x^{1.1})^{1.2} - x^{1.1\times1.2}$ into Wolfram Alpha and the graph it displayed was not $y=0$, contrary to my…
PKBeam
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Express $4^8+6^8+9^8$ as a product of 2 numbers, each greater than 100.

I attempted to factor it into $(4^4+3^4)^2$, but that gives a product of 2 times what is needed. Am I supposed to factor it, and how?
Gerard L.
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Solve equation with x in the base and x in the exponent

For Example: $5+5x=4\cdot 1.03^x$ My Question is: Is there a mathematical way that lets me solve equation where a $x$ is in the base and in the exponent?
ashold7
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