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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Exponents with the power being a negative/decimal?

How would I do the equation $b^{n}$ Or $b^{-n}$ Where $b$ is the base, and $n$ in a negative/decimal?
warspyking
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calculating a decrease at constant instantaneous rate

If we have a value e.g. $$ B = 20000 $$ and it decreases at a constant instantaneous rate of say $$ -1.1*10^{-2} $$ per unit time. What would B look like over say 300 time units, and how do we calculate this decline?
user1320502
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Plotting nth root of x against nx on a graph.

I've spent the last two days trying to figure this out. What I'm trying to do is rearrange this: $$ x^n = \frac xn $$ to make n the subject, to allow me to plot on a graph, with n being the y-value and x being itself.
Jamie
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Methods to calculate powers in my head

How can i calculate powers in my head, like small powers. for example $0.5^3$, how can i work this out quickly and easily? or $4^5$
I hate math
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Distributing exponents to variables

I am studying parabolas, but the way exponents are distributed is confusing me to oblivion. $(y_2 – 2)^2$ $y_2^2 – 4y_2^2 + 4$ I do not understand how can the first expression be simplified to the next. Could someone please provide an explanation?
user3758041
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Find numbers who compose the sum of sequence numbers(nth root)

I have an sequence of numbers 1, 2, 4, 8, 16, 32 and so on. Given an number, which must be the sum of the sequence, for example: 44(which is the sum of 4+8+32). How do I know the number 44 is composed by 4, 8 and 32? I suck at math, and I think most…
user163889
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Dividing 1 by powers of ten

I have something like, say, 3.9 x 10^-22 and I want it to be divided by 1. This is common in Chemistry science questions, but I fail to get the thing. How can we divide 1 by 3.9 x 10^-22 and get a proper answer? I mean, I get confused. Thank you for…
Mission Coding
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Describing the exponantiation of a number by itself

When a mathematician says What is the square of $n$? It is generally understood that the expected answer would be to multiply $n$ by itself, $n^2$. Is there a word analogous to square to describe the operation of multiplying $n$ $n$-times, $n^n$?
gxtaillon
  • 103
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Exponents with variables inside exponents

I am confused about how to reduce this, is there any way? $\sqrt x \ln(\sqrt x) = ln(\sqrt x^\sqrt x) = $ $?$ This can be written like this too: $ln(x^\frac{x^\frac{1}{2}}{2}$) Or: $ln(x^\frac{\sqrt x}{2}$)
JeremiahBarrar
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Non-integer exponents of negative numbers?

There is a formula for exponents of negative numbers as follows: $m^n=(-1)^n|m|^n$. This formulation works when $m<0$ and $n\in \mathbb{Z}$. But what about for $n\in \mathbb{R}$? Is there a simple way to define non-integer exponents of negative…
Aidan F. Pierce
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Exponential equation help

Solve $x^{ln x} = e^{(lnx)^{3}}$ I'm looking at the mark scheme but I don't understand what they've done. I'd appreciate it if someone could explain every step. MS: taking ln of both sides or writing…
Jim
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How to solve an exponential function with multiple addends

Our math teacher gave us the following exponential equation to solve: $3^x+10=2*7^x$ ...and I was stumped. Eventually, the solution given was to graph both sides and find their intersection using a calculator. But that solution doesn't satisfy me.…
gengkev
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Why 1.66x10e-27 is 1.66e-26

I am confused with this new way of writing exponential. For example I saw a question where person has changed 1.66X10e-27 to 1.66e-26. I am confused how -27 is reduced to -26 thanks
ZafarYousafi
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another question on surds and how to use math symbols in this site

$$\sqrt{ 3x }= x + \sqrt {3}$$ this is what i tried $$\sqrt{ x }= (x + \sqrt {3})^2\\ = x^2 + 3 $$ Give x in the form $$A \sqrt {B} + C $$ Can you show me how this is done step by step. The answer I have in the book is: $$\frac {1}{2} \sqrt{3} +…
user133745
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Need help with self study on surds

give x in the form A $ \sqrt B$ + C $(\sqrt 3x) = 3$ can someone show me how to solve this please?
user133745
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