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.

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order of operations with many level exponents

I was wondering, what is the order of operations when it comes to multi level exponents. Couldn't find anything in google. Something like: $$n^{n-1^{n-2^{\cdots^1}}}$$ In this case, if n equals 4, would it be correct to assume that 4^(3^(2^1)) is…
Reinis
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Solving $e^x + x = 5$ for $x$ without using a numerical method?

Canadian economist Mike Moffat asks on Twitter: Math nerd Q: Is there a way to solve $e^x + x = 5$ for $x$, without using a numerical method?
Borror0
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What comes after exponents?

We use multiplication for repeated addition, and in turn use exponents for repeated multiplication. What topic comes after this, for repeated exponentials? Is there something my teachers are hiding from me?
Monte Carlo
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Evaluate $\frac{(5+6)(5^2+6^2)(5^4+6^4)\cdots(5^{1024}+6^{1024})+5^{2048}}{3^{1024}}$

Evaluate $$\frac{(5+6)(5^2+6^2)(5^4+6^4)\cdot\dots\cdot(5^{1024}+6^{1024})+5^{2048}}{3^{1024}}.$$ I can't figure out where to start. I tried using logarithms but I couldn't get a pattern going. Any advice will be helpful, thanks in advanced.
Joshua Bonet
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Two solutions to one number.

I met a question which said : Find the value of $\sqrt2^{\sqrt2^{\sqrt2^{\sqrt2^{.^{.^{.^{.^{.}}}}}}}}$ Now to start I declared $y=\sqrt2^{\sqrt2^{\sqrt2^{\sqrt2^{.^{.^{.^{.^{.}}}}}}}}$ Now this implies that $y=\sqrt2^y$ Now solving this equation we…
Mayank Mittal
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Is there an operation that takes $a^b$ and $a^c$, and returns $a^{bc}$?

I know that multiplying exponents of the same base will give you that base to the power of the sum of the exponents ($a^b \times a^c = a^{b+c}$), but is there anything that can be done with exponents that will give you some base to the power of the…
Mark Cidade
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Simplify $x ^ y + x ^ z$ to a formula with only one $x$

Is there a way to simplify $x ^ y + x ^ z$ to a formula with only one $x$? I know $(x ^ y)(x ^ z) = (x ^ {y + z})$, but how can it change in addition?
TheCoffeeCup
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How exactly do exponentials work?

Hi all I know that $5^1 = 5$, $5^2 = 25$, $5^3 = 125$. But why is $5^{1.5} = 11.180339887498949$ ? How did we get the number $11.180339887498949$ ?
Pacerier
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how to calculate 2^1.4

So I have got a very basic question but it didn't come up as a google search so I am posting it here. I want to know how to easy calculate 2^1.4 = 2.6390... Using log and antilogs i.e not easy approach ? i.e. log y = log m^n log y = n log m log y…
Prateek
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negative exponent problem

$$\sqrt{\frac{1}{3^0 + 3^{-1} + 3^{-2} + 3^{-3} + 3^{-4}}}$$ Does this equal = $$ \begin{align*} & \sqrt{3^0 + 3^1 + 3^2 + 3^3 + 3^4} \\ =&\sqrt{1 + 3 + 9 + 27 + 81} \\ =&\sqrt{121} \\ =&11. \end{align*} $$ The answer is apparently $\frac{9}{11}$…
Jwan622
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Easy exponents question

I have the GRE Friday... I got hung up on this easy exponents problem (I think it was these exponents, don't recall exactly) $$\frac{6^{14}}{2^7 \times 3^5} = ? $$ The answer is $2^73^9$, but could anyone double check for me?
user3871
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Last three digits of 23^320

What is the best way to compute the last three digits of $23^{320}$? I know one way is by starting of $23^2$ and finding the last three digits, then squaring those (calculating $23^4 \pmod {1000}$) and getting the last three digits and so on until…
1110101001
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How to calculate $(a + b)^n$?

I'm trying to review and improve my math using Khan Academy. I'm now beginning to play with derivatives. Calculations like $(x + h)^n$ tend to come up often. I found out empirically that $(a + b)^2 = (a^2 + b^2 + 2ab)$ and a vague memory from school…
Alex Marandon
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Does $x^{n/n} = |x|$?

Just a couple of small technical point here. If x and n are real numbers, do we have to write $x ^ {n/n} = |x|$? Or can we just reduce it to $x^{n/n} = x$? One reason I ask is because then we would arrive at $x = x^1 = x ^{n/n} = |x|$. Does this…
John Daley
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Digits in a large power of two

I am trying to find the answer to: 2^34359738368. As to be expected every calculator and computer program I have used has crashed. To be honest I don't even want to know the exact answer, I just want to really roughly know the number of digits the…
Darcys22
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