Exponents Definition and 268 Threads

Suppose you have 8-1/3 and want a precise value for it. How would you go about calculating this on a regular scientific calculator. I punched in: 8, then the exponent button, then 1, then negative, then division, and finally 3. The calculator reads "error."

When multiplying x2 and x5, we get x7. Quick, dumb question: Why isn't it x10 instead (since we're multiplying and not adding)?

Hello, this isn't really a physics question but I'm getting pretty desperate and you guys have always been able to help me out before :) 1. Homework Statement http://imgur.com/mYtJDLI Homework Equations I believe I'm suppose to use the Laws of Exponents. For the first set possibly but not...

How can the properties of rational exponents be applied to simplify expressions with radicals and rational exponents?

Homework Statement Solve the following equation: 2^3+2^3+2^3+2^3=2^x[/B]Homework Equations log(a)^x=x*log(a)[/B]The Attempt at a Solution What i attempted was to log both sides, bring down the exponents, and summarize them. This left me with 12*log(2)=x*log(2). I then divide both sides by...

Homework Statement (-64)^(3/2) Homework Equations None. The Attempt at a Solution There is no answer that can be reached and it is supposed not be a real number. I was wondering why that is. How is it that there is no "real" answer to this problem?

I can most of the time successfully convert between base 10 and another base or another base and base 10 or between 2 bases where one of them is a power of the other(like base 2 and base 4 or base 3 and base 9). With negative bases I sometimes don't get what I want in that negative base and...

Alright here's my confusion, if i take say 3x^2 + 4x^2 ill end up with 7x^2 which i accepted was the correct way to think about it, but if i try the same problem without the x variable doing the same method, 3^2 + 4^2 = 7^2 this is obviously not the correct answer. Instead 3^2 = 9 and 4^2 = 16...

If you divide 333333 by 33, what is the value of the remainder? I'm not sure where to starte since this number can't be put into a calculator. Is there something with logs? I was thinking of bringing the number down with logs to 333log333, but I'm confused as to where that will lead me.

When one was reading some review books for engineering mathematics one has come across that kind of notation, below, and where to find books or materials that deals with these kinds of exponents, they look like this>> x^3x+2.

Hi all. I have been trying to understand propagation of error of exponents. Most an. Chem textbooks I see say y = a^x, sy/y = (sa/a)*x. But say y = a*b, then sy/y = ((sa/a)^2 + (sb/b)^2)^.5 . if a = b then sy/y= (2*(sa/a)^2)^.5 = 2^.5*abs(sa/a). This shows the rule y=a^x, sy/y= x^.5*abs(sa/a).

I mean why is f=ma? why not m0.123a1.43 or some random non integers? I hope you understand that my doubt doesn't limit just to force or energy or velocity e.t.c. it also extends to area of a square,circle e.t.c and all other formulae i think whole thing starts with direct proportionality.

1. Homework Statement (2.5 x 10^24)(4.5 x 10^-9) / (3 x 10^4) Homework EquationsThe Attempt at a Solution [/B] I know that when multiplying base ten numbers with exponents you add the exponents (ie: 10^2 x 10^3 = 10^5) ad that when dividing, the exponents are subtracted. I'm not sure what...

This might be a pretty stupid question. But why is it that while applying limits to an exponential function like- \lim_{x\rightarrow 0} e^{f(x)} we move the limit to only the part of the expression which involves the variable on which the limit is being evaluated and hence we now write it as-...

##cosθ + isinθ = cos(θ + 2kπ) + isin(θ + 2kπ)## for ##k ∈ ℤ## ##[cosθ + isinθ]^n = [cos(θ + 2kπ) + isin(θ + 2kπ)]^n## ##cos(nθ) + isin(nθ) = cos(nθ + 2nkπ) + isin(nθ + 2nkπ)## ##cos(nθ + 2mπ) + isin(nθ + 2mπ) = cos(nθ + 2nkπ) + isin(nθ + 2nkπ)## for ##m ∈ ℤ## Now consider the special case ##n =...

This might be a silly question and an obvious one, it's something I just wanted confirmation/clarification on. I've been recently reading a lot of mathematical papers/journals from around the world and have noticed something in particular. A lot of formulas or things they are postulating use...

Just curious, since we're discussing them this week in my class. Why do we need logarithms? Aren't they just a concoction to express exponents?

Hi Guys and Grillz Im not sure how these forums work, but if someone could help me real quick by explaining me how i should count this (3x2y)^8 (2xy)^3. I am sorry if i asked a dumb question or posted it in the wrong place. This is my first time doing this. :D

Homework Statement 81^5>32^x Find the maximum value of x in order to satisfy the inequality. Homework Equations Inequalities, indices The Attempt at a Solution Try to make the bases on both sides of the inequality same.

Hi, Let $n >6$ be a perfect number (A number $n$ is called perfect if $s(n)=2n$ where $s(n)$ is the sum of the divisors of $n$) with prime factorization $n=p_{1}^{e_{1}}p_{2}^{e_{2}}\cdots p_{k}^{e_{k}}$ where $1<p_{1}<p_{2}<\ldots <p_{k}$. Prove that $e_{1}$ is even

With only only paper & pencil (no calculator or logarithmic tables), figure out which of the following expressions has a greater value: 101/10 or 31/3. Please make use of the spoiler tag and write out your full explanation, not just the answer.

I hope I'm doing this correctly! I'm having problems understanding negative exponents and how they work... I have this problem, (x^-2)/(x^-2 + y^-2) I don't understand how the answer could be, (y^2)/(x^2 + y^2).. Maybe I'm doing something incorrectly? :/

Does anyone remember/know what the lowest co-efficient is of the imaginary part of the exponent for infinite Riemann zeta sums? I think it's (9/2)*pi, but I'm not sure.

Homework Statement Obtain the critical exponents for specific heat, susceptibility, and the order parameter (magnetization). Homework Equations $$A = -k_B T N \ln \left[e^{\beta J} \cosh (\beta h) +\sqrt{ e^{2\beta J}\sinh^2 \beta h + e^{-2\beta J} }\right]$$ $$\left<m \right> \propto...

1. I need some help understanding ratios between 2 numbers/quantities og exponents: [b]2.Here is the problem, When you take the ratio between 100grams and 1000grams it is 100g/1000g = 0,10 and you can convert this to kilos 0,1kg/1kg = 0,10 and the ratio stays intact, that makes sense. But...

How does 2^5/2 become 2^2 multiplied by 2^1/2? (The '^' means 'to the power of' so 2 to the power of 5/2. I am not sure how to write this as an exponent as this is my first post.) 2^5/2 = 2^2 × 2^1/2 So 2^2 = 4 and 2^1/2 means Square Root so there is a radical sign, so it becomes √2. I...

Hi, I am helping my kid with exponents. I told her that the exponent tells us how many times we should multiply the base number. While it works with a simple example like 4^6, I am not sure how to explain her why 4^0 =1 and why 27^(1/3) = 3. Any ideas? Thanks.

Hi everyone. I'm back and happy to be back. I missed math. Anyways, I am taking a college Algebra class as it has been a while, and I definitely want to make sure I have a good foundation for higher maths. But, I have a conundrum. The teacher today gave this example that I thought I had solved...

Hi, I've been reading about critical exponents and how they're related in any system. I've seen how, for example, several exponents can be extrapolated from charts using a log-log fitting. I would like to know how this procedure works exactly, I know it's a silly question but I've been...

I've always had trouble remembering things that are similar, but not the same, like sometimes you add exponents of an expression, is there something I can use to remember this?

an + bn/ an-1 + bn-1 = (a+b)/2 can we say n=1 by comparing exponents? is there any other solution of it?

can you help me find the derivative of: (5t^2+1)4 this is what I did: (5t^2)(ln 5)(2t) * 4(5t^2+1)3 did I do this right?

Homework Statement Suppose ##f(x)## and ##g(x)## \rightarrow 0 as x \rightarrow 0+. Find examples of functions f and g with these properties and such that: a.) ## \lim_{x\rightarrow 0+} { f(x)^{g(x)} = 0 } ## Homework Equations None The Attempt at a Solution Let ## f(x) = 2^x-1...

(9x)^-1/2 So, I'm not entirely sure how to go about this question. It's got a negative exponent, so I assume its 1 / something. My guess for the answer would be: 1 / 3x [(25xy)^3/2] / x2y For this question, would I compute 253/2 and then x3/2 y3/2 and then divide by x2y

$\displaystyle\frac{-9b^2(a+3b)^{m+2}(2b-4c)^{2+m}}{4(3a+9b)^{2m+2}(b^2-2b^2)^{2-m}}$ my answer to this is $\displaystyle-\left[\frac{2(b-2c)^2b}{9(a+3b)}\right]^m$ i used some factorization of some quantity to arrive to this answer. but I'm not sure how did that technique works. for...

Homework Statement Simplify (x-2 - y-2) / (x-1 + y-1) Homework Equations The Attempt at a Solution So I just factorised the numerator into x-1 - y-1 and x-1 + y-1. And was left with x-1 - y-1 as an answer. The textbook gives (y - x) / (xy) as the answer (no working shown). So...

Basically I don't know anyone in real life that can help me with this, so I need help checking to see if my answers are correct :) PART A 7) Simplify (5x^3yz^2)^2(-3x^3y^4z) My answer: -75x^9y^6z^5 8) Simplify the problem below using positive exponents only. 8a^-2b^3c^4 18a^5b^-3c My...

In Monte Carlo simulation of classical spin systems I have a trouble to determine critical exponent ##\alpha##. ##M \propto L^{-\frac{\beta}{\nu}} ## ## \chi \propto L^{\frac{\gamma}{\nu}} ## ## C_V \propto L^{\frac{\alpha}{\nu}} ## Is this correct? From that slope of the curve ##\ln Cv## as a...

Homework Statement If a solution containing a heavy concentration of hydrogen ions(i.e., a strong acid) is diluted with an equal volume of water, by approximately how much is its pH changed? (Express (pH)diluted in terms of (pH)original.) Homework Equations I think the question...

Hello everyone, I am a bit confused about definitions rules. I can have more questions but for now I want to ask only one question: Let us say I have a number: \sqrt[6]{3x3x3x3x3x3} 3x3x3x3x3x3 is equal to both 27^2 and (-27)^2. But If I write these two expressions separately I can get...

Homework Statement Why is ##(-1)^{n+1} (-1)^{n+1} = (-1)^{2n+2}## but ##(-1)^{n+1} (1)^{n+1} = (-1)^{n+1}## I thought in both instances you are to just add the exponents. Homework Equations The Attempt at a Solution

The question was: How many real number solutions are there for 2^x=-x^2-2x. I tired for an hour to isolate x but i couldn't do it. Then i used wolfram alpha and it gave me two solutions and graph. I realized that question was, how many not what are the solutions, and i could do that by graphing...

Okay so I'm in Calculus 1 and we are working on derivatives. I understand it all but I have been having some trouble with some basic math skills that I cannot remember from high school and I can't seem to find a good tutorial anywhere online. I am having problems with multiplying fractional...

Hi, I have an algorithm that I have to test, and it gives me certain variables at different stages of time. I also have a "result" (I guess you can call it that), that these variables are supposed to amount to, in some mathematical fashion, at those equal points in time. This gives me a...

Homework Statement By mathematical induction, prove that for n ≥ 1, 4/(7n - 3n). Homework Equations The Attempt at a Solution I got the base case down P(1): 7-3=4. Now the actual problem, 7n - 3n = 4x 7n+1 - 3n+1 = 7(7n) - 3(3n) =7(4x + 3n) - 3(7n - 4x) =21x+ (7(3n)) - (3(7n)) + 12x -This...

The way i am evaluating post fix expressions is not working with exponents Example InfixII 3*(4^2-2/3)+4 To post fix 342^*23/-4+ =16*3-2/3)+4 Am i evaluating the parenthesis the wrong way

Homework Statement Determine if sequence converges or diverges, if it converges find its limit. a (sub) n= (3^(n+2))/(5^(n)) The Attempt at a Solution The only things I've tried doing thus far is setting the sequence up as a function and letting x approach infinity. I then tried using l...

Hi, If all x,a,b and c are all natural numbers, is this true? x^{a^b} = (x^{a^{b-1}})^a Proof if c = a^{b-1} ca = (a^{b-1})a = a^b and (x^c)^a = x^{ca} = x^{a^b} Could I please have some feedback on this, Thanks

Homework Statement (2x+3x)/6x = 2-x+3-x I've tried moving the 6 above, splitting it up and so... but i can't figure how to do it. It must be pretty simple, but I am just not seeing it. all helps appreciated!

suppose we have ab why must 'b' be dimensionless? Mathematicians have defined crazy things over the centuries so why haven't they defined this one?