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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Quick check on multiplied powers

I'm feeling a little silly askign this question, but after about 2 hours of circling around the same point I am getting frustrated. Starting with the expressions for $M$ and $R$ from the lecture…
Michael Roberts
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Variables and exponents

How would you solve this equation ? $$500n=4000(1.016)^n$$ I tried using some logarithms but I could not do it. The only unknown variable is n but I'm having a bit of trouble getting there.
G Skeet
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Simplifying algebraic fraction, exponents

Would someone be able to tell me how $$\bigg( \frac{5}{a^4} \bigg)^{-3}$$ gets simplified to $$\frac{a^{12}}{125}?$$ Thank you!
Spica
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How would I calculate sum of digits in the number (a^b)?

I was doing a question from a site,project euler specifically.I came to a question in which I was asked to calculate sum of digits in number 2^1000.Since I program very often I was able to do that question by making array and calculating as We used…
thoughtful me
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Given: $C=10$, $C^a=3$, $C^b=5$, how to solve $C^{2a-b+1}$.

Given: $C=10$, $C^a=3$, $C^b=5$, how to solve $C^{2a-b+1}$. I would be very grateful if somebody show me how to solve this. Thanks.
Alex
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How to solve exponential expressions?

There are some questions that I have. Question 1) $$ (x^2/5)^3 = 2^6/5^y$$ To find the $y$ I used the same base $$ 1/5^3 = 1/5y$$ Teacher told that the exponent will be the same if equaled, so $ y = 3$. What my question is how would I find $x$??…
MATH ASKER
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Question about the identity of $2^{2^n}$

Is this identity true: $2^{2^n}= 4^n$? I believe this is true as far as I know. Sorry this is the only place to ask. Is there another identity for $2^{2^n}$ which I can simplify to?
Ka Wa Yip
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Best way to solve $24^{100} \times 1.5^{50} \times 12^{-149}$

I think I could solve this but I would like to know the best way to do it with the least amount of calculations
Hamza Benchekroun
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x to the power of an irrational number

If one were to graph the function of $$ f(x) = x^e $$ How would this look? (With explanation as to why) Particularly in the case of negative x values.
Henry Walton
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If $3^{33}+3^{33}+3^{33}=3^{x}$. Solve for $x$.

If $3^{33}+3^{33}+3^{33}=3^{x}$. Solve for $x$. So we have: $$3^{33}+3^{33}+3^{33}=3^{x}$$ I added the left side and obtained: $3(3^{33})=3^{x}$ The problem I have is that extra $3$. If not, I could have said $x=33$. Any hints in how to proceed with…
Caddy Heron
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If $x^{x^4}=4$. Find $x^{x^2}+x^{x^8}$

If $x^{x^4}=4$. Find $x^{x^2}+x^{x^8}$. I found this one in a competitive exam paper and found it interesting. Thanks for any help.
Soham
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What kind of operation/rule was applied here?

Maybe this is a typo in our assignment and solution, but I can't tell. The question: The solution: What happened here with the minus signs in the first factor and in the exponent? Edit: the assignment asked for the fourier transform of $f(x)$. So…
Reto Höhener
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0's Exponents are impossible?

I've had something that's been bugging me, and I tried research and asked my math teacher. None had sufficient answers. The concept of $0$ is that when $0$ goes to any exponent except for $0$, it becomes $0$. For example, $0^3 = 0$, but $0^0 =$…
Gil Keidar
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What is $R^0$ when $R=0$?

We say that for a number $R$, $R^0 =1$, but if $R=0$ how can $R^0$ be $1$?
user253897
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Comparing two large numbers

Can you compare two large exponential numbers, like $5^{44}$ and $4^{53}$ without taking their logs?
dexter
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