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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Complete the square for exponents

How does $\exp(2x)-2+\exp(-2x) = (\exp(x) - \exp(-x))^2$ ? I am having trouble using complete the square.
user174232
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Solving $x^\frac{1}{x}=y$ for $x$

I've tried everything: Taking $\ln$ of both sides, raising to the power $x$, nothing seems to work. Is there a way to solve this or am I going to have to use numerical methods instead?
itdoesntwork
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If $10^{80}=2^x$, what is the value of $x$?

If $10^{80}=2^x$, what is the value of $x$? (Or, what binary word length would you need to contain $10$ to the $80$?)
RoboJ1M
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Proof that irrational exponents exist, and are unique?

Can someone provide a proof that for any given irrational number, $b$, exponentiation by that number defined as a limit of rational powers always converges, and that if we choose a particular base, $a$, that the no two $b$'s yield the same limit. (I…
user82004
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How to solve $x^x=k$?

Possible Duplicate: $x^x=y$. How to solve for $x$? If we have $x^x=4$ it's easily solved by substituting $x$ with $2$. But for general equation like $x^x = k$, how we can find the solution? Moreover, what if we have equation $$x^{a+bx}=k$$ or…
Mas Adit
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Finding the value of $x$ for an equation

If we have the expression $a=x^{c\cdot x+1}$ where the values of $a,c$ are known, how can we find the value of $x$? I tried using log but it yields: $x = a ^ {(1/x)/(c-1/x)}$ from which I can't find any solution. Thanks.
pranay
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Reducing exponents with a common base when terms are added

I have a series of terms as follows: $$e^{6x\pi.0} + e^{6x\pi.2} + e^{6x\pi.4} + e^{6x\pi.6}$$ Obviously the first term is just 1 but is there a way to specify the terms in one single term or shorten it somehow other than just 1 + ...? i is an…
Noel Evans
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Why is X raised to the power of 0 = 1?

So as the topic states, why is 5^0 = 1 and not 5 or 0? Is it only because the other exponential laws wouldn't work if it was not the case?
user128522
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How to find out the value of numbers having fractional powers

How to find out the value of numbers having fractional powers manually without using logarithms and calculators?? For example : $2^{1.6}, 3^{2.1}, 5^{3.22}$ etc, I know we can find out the value using logarithms. But I want to know how to find out…
Shiva
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Prove that $(b^m)^{1/n} = (b^p)^{1/q}$ if $r = m/n = p/q$

I'm working through Rudin's "Principles of Mathematical Analysis" on my own, so I don't want the full answer. I'm only looking for a hint on this problem. The problem states that $b > 1$ and $m, n, p, q$ are integers, $n > 0$, $q > 0$, and $r = m/n…
M T
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Exponent rules with negative numbers

Hello if you could answer this please what is the difference between -2^2 and (-2)^2
Derrick
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This looks like a simple exponent, but how to solve it?

Can anyone help with finding the $x$? $$\frac{998^{999}+998^{998}}{998^{999x}}=999$$
Haura QA
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Exponents and Parentheses

Can $(-25^{44})$ be rewritten as $(-1) (25)^{44}$? Will the exponent 44 affect the (-1) because of the parentheses? Or does the 44 need to be inside the parentheses: $(-1) (25^{44})$? Thank you!
GardenRoses
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Addition of numbers with same base but different exponents

The problem itself is $(288\sqrt{3})^{1/5}+(288\sqrt{3})^{4/5}$. The answer is supposed to be of the form $a+b\sqrt{c}$, but I have no idea how to simplify it.
user79199
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Does the product rule for exponents apply to a power of a power?

Does the product rule for exponents apply to a power of a power? For example: If I have 3^(4^5), will that be equal to 3^(4^2)*3^(4^3)?
Diamoniner12345
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