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
2
votes
3 answers

How can I determine a formula for an exponential ratio?

I am not very experienced in mathematical notation, so please excuse some terminology misuse or formatting shortcomings. I have a project in which a value needs to increase from a set minimum to a set maximum in a set number of seconds. It is easy…
JYelton
  • 137
2
votes
1 answer

Exponential function: Change base to exp

Why is the following true? $$\left[\frac{N - it}{N}\right]^{j+1} = \exp\left(-\frac{ijt}{N}\right)$$ i,j - integers less than N. Is there any theorem which allows me to get this result? I tried with $$N=2^{32}, i=j=2^8, t=2^{16}$$ and its almost…
Yola
  • 1,665
  • 1
  • 18
  • 31
2
votes
4 answers

Raising to rational power - issues

Raising a real number to a rational power is very simple, right? Consider the following example: $$−27 = (−27)^{\frac{2}{3}\frac{3}{2}} = ((−27)^{\frac{2}{3}})^\frac{3}{2} = 9^\frac{3}{2} = 27$$ The issue arose because of this part:…
user216094
  • 945
2
votes
1 answer

Convert $3^n$ to some form of $2^n$

I am not from Maths field, but I need your help to convert the $3^n$ form to $2^n$. I need to change the base from $3$ to $2$. The resultant expression can be of any form.
Shahbaz Ahmad Sahi
  • 23
2
votes
3 answers

relation between exponent values and solution

If $a,b,c$ and $d$ are positive integers such that $a^5=b^6$ and $c^3=d^4$ and $d-a=61$, then find the smallest value for $c-b$. $d-a=61$, so $d=a+61$ or $a=61-d$. But then how to substitute these values in the equations and solve? I am stuck.
Hari
  • 153
2
votes
2 answers

Solve the inequation for $x$

Solve for $x$ : $ (x-1)^{2005} x^{2006} (x+1)^{2007} \le 0 $ I tried cases like : $ x-1 \le 0 $ , $ x \le 0 $ , $ x+1 \le 0 $
Bogdan15
  • 81
2
votes
2 answers

sum of the digits of the number $(5^{2015})(2^{2018})$

What is the sum of the digits of the number $(5^{2015})(2^{2018})$ So I am guessing, I have to find out the product of $(5^{2015})(2^{2018})$ and add each digit of the product. The question is how do I find the product of $(5^{2015})(2^{2018})$.…
Caddy Heron
  • 1,249
2
votes
2 answers

Need assistance in solving exponential equation: $\frac{27^x}{9^{2x-1}}=3^{x+4}$

Find value of x: $$\frac{27^x}{9^{2x-1}}=3^{x+4}$$ My steps: $$\frac{(3^3)^x}{(3^2)^{2x-1}}=3^{x+4}$$ $$\frac{3x}{4x-2}=x+4$$ Please help me finish solving, and correct me if what I did so far has mistakes. Thanks very much.
Arthur Alex Karapetov
  • 409
2
votes
1 answer

How to determine efficiently if the arithmetic addition and subtraction of certain powers of N can be equal to M?

I am given a number N and another number M . I have to find out if arithmetic addition and subtraction of certain distinct powers of N can lead to formation of number M . I tried different approaches , but not any reliable one. Also, we can use one…
user249117
  • 245
2
votes
3 answers

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?
ReliableMathBoy
  • 968
2
votes
1 answer

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!
NeilRoy
  • 2,091
2
votes
2 answers

Why do I get two times the base if it's squared when I multiply the value by four?

For example, if I multiply the value of a base squared by four, I also get twice the base if it's squared. Look:$$6^2\cdot4=12^2$$ because $$36\cdot4=144$$and $36$ is the square of $6$ and $144$ is the square of $12$. Why does this always happen?
ReliableMathBoy
  • 968
2
votes
1 answer

Why doesn't $2^2 = -4$?

I was just curious because a number raised to the $\frac 1x$ where $x$ is an integer greater than $1$ has $x$ solutions, why can't a number to the $x$ where $x$ is an integer greater than $1$ also have $x$ solutions?
Guest
  • 39
2
votes
3 answers

Why is x^(a/b) equivalent to the bth root of x raised to the a power?

I was wondering if someone can tell me what the logic behind converting fractional exponents to radicals is? For example, the exponent 1/2 is a square root, 1/3 is a cube root, and 2/3 is the cube root of x squared and so on. Can someone explain…
Little Black Dog
  • 161
2
votes
3 answers

Real analysis of powers

Show that if $a,b$ are rational numbers and $x$ is a positive real number then $x^a$$x^b$ $=$ $x^{(a+b)}$ I honestly have no idea how to even do this. Anyone have any hints or a good explanation? Thanks in advance!
Zoë Soriano
  • 181
1 2 3
…
35 36