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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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How come negetive base raised by exponent can be two answers?

Following by Exponent rules, I got really confused. I notices the following: $(-1)^1 = 1$ so $(-1)^{2\cdot0.5} = -1$ Now,I can get two different answer: $((-1)^{0.5})^2 = (\sqrt{-1} )^ 2 = i^2 = -1$ or $((-1)^2)^{0.5} = (1)^{-0.5} = \sqrt1 =…
ItayNG
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How to decompose an exponent?

If i have an function: $$f(x) = x^a$$ after, i solved an equation: $$1/x^{an}$$ so, how i can decompose the exponent to get the equation based on my previous function $$f(x) * x^n$$ this is a error, because $$x^a *x^n = x^{a+n}$$ But i need,…
Eduardo Campos
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Solving y in exponentiation

I'm already long time from school. I want to solve y from this equation: $x = 10^\frac{(y - 109)}{32}$ How can I do that? In real life y is the rain intensity, and x is number of millimeters rain per hour.
Robbert
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When you flip a fraction to remove the negative exponent, do you flip all of what's on numerator and denominator?

When you flip a fraction to remove the negative exponent, do you flip all of what's on numerator and denominator? Or do you only do that with variables Such as: (-7a2b3c0/3a3b4c3 )-4 Will it be written…
schoolwithschool
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What is the property called that says that $a^x = a^y$ iff $x = y$?

I was just wondering why two numbers $a^x$ and $a^y$ are equal only if $x = y$ ? Which power-law is this?
Msmat
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What are these numbers called?

Say I have numbers that are all multiple of 2, I would say, well they are multiples of two. How are numbers $x$ called with respect to $a$ that are all formed like $x = a^b$? I am assuming here that $b$ is a positive integer.
kutschkem
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Is it true that $0^r =0$ for all $r > 0$?

Is it true that $0^r =0$ For all $r > 0$? It comes in the context of real exponentiation as most of the text (e.g. Tao Analysis 1) defines $x^y$ for $x>0$ and not for $x=0$ when y is arbitrary real number
Jave
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Could somebody help me solve the following equation

Could somebody help me solve the following equation for x and y: $7^{2n - 3}\cdot 7^{3}\cdot 7^{n + 3} = 7^{xn + y + 1}$ I reached a step where: 3(n + 1) = xn + y - 1 but can't figure out how to proceed :-(
Mario Christov
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How to find the units digit of 2^102

I'd like to answer this question without using a calculator. My first instinct is to find a pattern in the value of $2^k$: $2^1 \equiv 2$, $2^2 \equiv 4$, $2^3 \equiv 8$, $2^4 \equiv 6$, $2^5 \equiv 2,...$ So units digit repeat with period $4$…
Cyzanfar
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Reverse continuous compound interest formula (solve for r)?

The continuous compound interest formula is pretty simple: $$ A = P*e^{rt} $$ But how can I solve for $r$? Wolfram|Alpha introduces this variable $n$ out of thin air, plus imaginary $i$ which I'm not sure is necessary or not if we can add a few more…
mpen
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why the relationship between A^i vs A^-i

I am trying to get an intuitive idea of imaginary exponents. I've read this: Understanding imaginary exponents and one thing I am wondering is why if $A^i=x+iy$ then $A^{-i}=x-iy$ I read the comments in the link, but the answer someone gave may be…
Mike
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Confused about exponent rule.

I feel very dumb asking this. I'm trying to calculate $e^{\pi i n/4}$ for odd $n.$ I say the following: $e^{\pi i n/4} = (e^{\pi i n})^{1/4} = (-1)^{1/4}.$ However, Wolfram Alpha says that for $n = 5$ we have $-(-1)^{1/4}.$ I am confused.
green frog
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Find the minimum value of $x+y+z$ for positive exponents $x,y,z$?

$x,y,z$ are positive integers, for equation $$2^{3x}+2^{5y}=2^{7z}$$ find the minimum value for $x+y+z$. I am not sure is it possible to find all $x,y,z$ pairs. If so, can you provide a strategy for it?
user373239
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$\frac{25^x+125}{6}=5^{x+1}$ what is the value of $x$?

It is just the title, $$\frac{25^x+125}{6}=5^{x+1}$$ What is the value of $x$? Thanks.
JamesB
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Exponentials to the negative power

Could someone please help me in showing how $$xe^{-nx}\le\frac1n$$ I don't totally see why the LHS is bounded by the RHS. Thank you.
USERMATHS
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