Questions about exponentiation, the operation of raising a base $b$ to an exponent $a$ to give $b^a$.

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-1
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0answers
17 views

Raising x to an odd power that's at least 3 or to an even power that's at least 2 [on hold]

Whenever I raise x to an odd power of at least 3, I get a squiggle as somebody calls it and whenever I raise x to an even power that's at least 2, I get a parabola and if the power is higher, its left ...
-2
votes
1answer
19 views

Hypercubes, exponential functions [on hold]

Kyle is trying to write an interactive computer program that draws cubes in any number of dimensions. From his research, he found that the number of the form n^4 with an an positive integer is called ...
1
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1answer
38 views

Two hard indices questions, (what is power to a power of fraction) and (how is $(2^x)^2 = 4^x $)

The answer for question 1) is $2^{3b+6}$ Question 2 I only don't get the $Y^2$ bit
0
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1answer
25 views

Why does the graph of an exponential function shoot straight up when getting to x=1 in an exponential growth function with x^huge number?

I used to notice that when x is raised to the power of a huge number, the graph shoots up at x=1. Why does this happen?
3
votes
1answer
34 views

Why an exponential graph can't have b equal to 1

I've seen that the graph of an exponential function, $f(x) = a\cdot b^x$, cannot have $b$ equal $1$. Why is this? I think it's because the function would be a flat line if $b=1$. Is this true?
1
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3answers
38 views

Any reason an exponential decay function approaches but doesn't cross the x-axis?

I've seen graphs of exponential decay functions (where a>0 and 0 is less than b is less than 1) and they don't seem to cross the x-axis. I think it's true. Any reason this happens?
2
votes
1answer
31 views

Confusion about exponents like ${x^m}^{(1/n)}$.

I've been reading this post. It says that $\sqrt[m]{x^n} = x^{n\frac 1m}=x^{\frac mn}=x$ if $m=n$. Let's take $x=-2$, and $m=n=2$. Now we have, $\sqrt[2]{(-2)^2}=\sqrt[2]{4}=2$ But according to that ...
5
votes
3answers
102 views

Does $1^i$ and $1^{\frac{0}{0}}$ also give $1$ again? [duplicate]

This is the property of Real number $1$ that, $1^n=1$ does this property only hold $\forall n \in \mathbb R$ or also $1^i=1$ and $1^{\frac{0}{0}}=1$ If it is; explain how? I think that it should ...
1
vote
2answers
37 views

Solve the exponential equation, by using $\log_{10}$ of of the sides of it. [closed]

Solve the exponential equation, by using $\log_{10}$ of of the sides of it. The equation is: $5^{x-1}=2$
3
votes
4answers
91 views

Why is $n^0 = 1$? [duplicate]

Why is any number to the zeroeth power equal to 1? I would think it would be equal to zero, since nothing multiplied by nothing is, well, I would think 0. But it is 1? Examples: $(-5)^0 = 1$; $0^0 ...
0
votes
4answers
44 views

Solve for $x$ given $2^{2x} - 2^{x+2} = 5$ [closed]

$$2^{2x}-2^{x+2}=5$$ I know I am being dumb, but I can't figure out how to factor this one. I need to solve for $x$.
1
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1answer
22 views

Exponent identities with imaginary exponents$\left(a^i\right)^i$

I've been trying to understand how imaginary exponents work, and I think I mostly understand it, but I'm confused by something like $\left(a^i\right)^i$ (where $a$ is real). According to the normal ...
5
votes
4answers
297 views

Compare three numbers, expressed as powers: $4^{68}$, $5^{51}$ and $12^{23}$

So I have these numbers: $4^{68}, 5^{51}, 12^{23}$ They need to be ordered from the smallest to greatest. I have no idea how to solve this. Typically, one should break down the exponents somehow to ...
1
vote
1answer
72 views

Solving a Diophantine equation: $y^x=x^{2007}$, $x$ and $y$ integers.

I found this Diophantine equation and to solve it I used the definition of logarithm but the solution doesn't require the use of logarithmic rules. I solved it in this way: $$y^x=x^{2007}$$ ...
1
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3answers
24 views

Algebraic simplification of likelihood ratio

Can someone help me understand how this: ...
0
votes
2answers
10 views

Properties of exponents when dealing with induction.

This will most likely be a simple question for most of you. While watching my lecture today the white board cut out and the instructor didn't explain the final step in an example. He went from ...
-1
votes
2answers
26 views

indices and powers

If $a^3 = b^2$, which of the following statements could be true? $a \lt 0$ and $b \gt 0$ $a \gt 0$ and $b \lt 0$ $a \gt 0$ and $b \gt 0$ Can anyone explain the answer with examples?
4
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1answer
22 views

Square Roots: Variables with Exponents.

Alright, so let me get this straight: $\sqrt{x^2} = |x|$ $\sqrt{x^3} = x\sqrt{x}$ $\sqrt{x^4} = x^2$ $\sqrt{x^6} = |x^3|$ Are these correct?
2
votes
3answers
52 views

Comparing the size of $(\sqrt{5})^e$ and $e^{\sqrt{5}}$

So I have to figure out which one is bigger between $(\sqrt{5})^e$ and $e^{\sqrt{5}}$. After some trial and error I've come to the conclusion that $(\sqrt{5})^e > e^{\sqrt{5}}$. But of course I ...
1
vote
0answers
66 views

Algorithm for tetration to work with floating point numbers

So far, I've figured out an algorithm for tetration that works. However, although the variable a can be floating or integer, unfortunately, the variable ...
3
votes
1answer
40 views

Why x by x is NOT equal to squared x within exponents?

Normally you can write $x*x=x^2$ But if you are operating within exponents, $a^{x*x} \neq a^{x^{2}}$ as the latter is equal to $a^{2x}$. Is it a problem of notation ? [Edited] Thank you to having ...
0
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0answers
32 views

Symbol for exponentiation of a sequence? (Equivalent to SIGMA for summation and PI for product)

I have a student asking whether there is a symbol for exponentiation of a sequence? So there's SIGMA for summation of a sequence, PI for multiplication of a sequence and perhaps something else for ...
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votes
2answers
43 views

What is e^e^x? Also, what is log e^e^x to the base e, i.e, ln(e^e^x)? [closed]

What is e^e^x? Also, what is log e^e^x to the base e, i.e ln(e^e^x)? Thank you.
3
votes
2answers
34 views

unsure how to rearrange $f(x)$ into suitable $p(x)/q(x)$

Consider the function $f(x)= (x^3 + 2x - 3) / (x^2 + 3x + 4)$ by dividing the numerator and denominator by the highest power of $x$ present, convert $f(x)$ into the form $P(x)/Q(x)$ where both $P(x)$ ...
2
votes
1answer
49 views

Is there any condition while applying law of exponents?

${[(-3)^2]}^\frac{1}{2}$ = ${(-3)^2}^\frac{1}{2}$ = $-3^1$ = $-3$ But counted other way it is $9^\frac{1}{2} = \surd{9} = 3$ where I went wrong?
6
votes
4answers
516 views

How do pocket calculators calculate exponents?

I'd like to know specifically how a pocket calculator (TI calculators also apply) calculates $e^{0.1}$, and what methods or algorithms pocket calculators use in order to produce their answer.
1
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1answer
34 views

Combining log terms

I have this particular problem. We have to combine the log terms into a single log term: $$\dfrac{(2\ln a- \ln b - 5\ln c)}{2}$$ I did it in the following way : $$''~= \ln a -\frac{1}{2}\ln b - ...
2
votes
2answers
43 views

When (and why) did the convention that exponents are evaluated from right to left arise?

Earlier, I saw this question on Quora: X^Y^Z Which one do I do first? and the current most-upvoted answer is this: The ^ operator is not associative, so that: (X^Y)^Z is not the same value as ...
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2answers
32 views

How many uranium-238 atoms are left after 1.338 x 10^10 years?

The half-life of uranium-238 is about 4.46 x 10^9 years. How many will there be after 1.338 x 10^10 years? How can I figure this out? I know it's exponential, but how?
1
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0answers
42 views

series of powers of integer powers

Given two real positive numbers $a,b\in(0,\infty)$ and a series of natural integers $n=1,2,3,\dots$, is there any known formula to apply in order to calculate the series $$s(n)=a^{b^n}?$$ My goal is ...
1
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2answers
34 views

Simplification of powers

I think this is a really simple question, but for some reason my brain can't get round it. I am proving a combinatorial result by probabilistic method and the last step has got me really confused. ...
1
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1answer
15 views

Confusion with repeated exponents

When someone writes: $3^{3^3}$ Do they mean $3^{(3^{3})}=3^{27}$ OR ${{(3^3)}^3} = 27^3$ ? There are no brackets Please reply ... this may be a silly question ... Thanks!
0
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1answer
34 views

Solving for single variable proving to be extremely difficult.

I have been at this equation for about two days now, and I can not for the life of me find a way to solve to i. If anyone can please show me a step by step into solving this, it would help me out so ...
1
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1answer
50 views

Example for $a^k\equiv b^k$ and $k\equiv j$ but $a^j\not\equiv b^j\pmod n$

I need some help in the number theory please , Who can give me an example : If $$a^k≡b^k \pmod{n}$$ and $$k≡j \pmod{n}$$ is not necessary to be $$a^j≡b^j \pmod{n}$$
1
vote
2answers
32 views

Gaussian distribution raised to a power

Given that $X$ follows a Gaussian distribution $e^{-x^2/2\sigma^2}$, what distribution is followed by $X^{1/3}$? How does one start to solve this problem? I guess it isn't ...
0
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0answers
17 views

Ask about description of exponent number.

I'm a Taiwanese student and face an English describe problem. My teacher told me " 1.34 x 10 of negative 4 exponent means 1.34 x 10^(-4)" in English description. And I wander why this exponent is use ...
0
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1answer
35 views

Factorals with exponents. Is their a way?

I know of multiplication factorials with the 4! = 4*3*2*1 and I know of the addition with the nth triangle. I am busy deriving my own equation for something, and i am getting stuck on how to furthur ...
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2answers
43 views

Question on power, If 2x^2x^2x^2x… =4 Solve for x

I've seen this random example, in which can anyone give me clue how to solve for $ x $ here?
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0answers
58 views

Inverse and named fixed values, with ↑↑?

The inverse of $+$ is $-$, of $\times$ is $/$ and of $\text{^}$ is Log. Continuing upwards hyperoperationally, what is the inverse of $↑↑$? Whats more somtimes values that are fixed are given ...
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2answers
61 views

Find remainder of $3^{12} + 5^{12}$ when divided by $13$ [closed]

What is the remainder when $3^{12} + 5^{12}$ is divided by $13$?
22
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7answers
3k views

Is $\exp(x)$ the same as $e^x$?

For homework I have to find the derivative of $\text {exp}(6x^5+4x^3)$ but I am not sure if this is equivalent to $e^{6x^5+4x^3}$ If there is a difference, what do I do to calculate the derivative of ...
3
votes
2answers
167 views

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 ...
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votes
6answers
95 views

Why does $(2^{20}+2^{20}+2^{20}+2^{21})=5\cdot 2^{20}$?

I did this question on artofproblemsolving.com and I do not understand the solution. Why do I have $5 \cdot 2^{20}$? Can anyone explain?
5
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1answer
117 views

For each irrational number $b$, does there exist an irrational number $a$ such that $a^b$ is rational?

It is well known that there exist two irrational numbers $a$ and $b$ such that $a^b$ is rational. By the way, I've been interested in the following two propositions. Proposition 1 : For each ...
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votes
1answer
67 views

What is 0 raised to 0 ???!!!! [duplicate]

I have read many articles on this confusion but i am still confused... My simple question is - What is $0^0$? What is the present agreement to this? I feel that it should be 1 as anything to ...
1
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4answers
53 views

Is the sum of two exponential function can be equivalent to a third exponential function? [closed]

What will be the sum of two exponential functions $2\exp(4 x) + 3 \exp(5 x)$ equivalent to a third exponential function? Is it possible?
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3answers
35 views

How to solve for f?

The question asks to solve for the variable: $$2=6(3^{4f-2})$$ I am not quite sure how to solve for $f$ because the bases on either side cannot be made equal. Here is an example of a similar ...
0
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1answer
34 views

Exponentiation for hash function & associativity

Some cryptographic papers use $H^n(x)$ to mean $H(H^{n-1}(x))$ where $H^0(x) = x$ and $H$ is a cryptographic hash. So $H^3(x)$ would be $H(H(H(x)))$. Is this definition formally correct? It seems to ...
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0answers
14 views

Evaluating Expressions with Integer Exponents

Simplify the expression by writing as a single power and then evaluate for a=-1,b=-2 and c=3. $$(b^{3}a^{4})^{2} \times (a^{3}c)^{3} \over ac^{3}$$ Here is what I did: ...
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1answer
25 views

Exponents with base close to $1$.

I was just fiddling around with a calculator and calculating powers of numbers really close to $1$ like $1.01,1.001\dots$ trying to find at what value they exceed $2$. This got me thinking if I could ...