0
votes
2answers
41 views

Simple question on exponentiation

I know this one is trivial, but I was wondering: if I have something like $$a^{b^c}$$ then i know that it should be read as $$a^{\left(b^c\right)}$$ if no other parenthesis is present. Question: if ...
0
votes
2answers
39 views

If $\sqrt{x+y}+\sqrt{y+z}=\sqrt{x+z}$, then $\frac{1}{x}+\frac{1}{y}+\frac{1}{z}=?$

If $\sqrt{x+y}+\sqrt{y+z}=\sqrt{x+z}$, then $\frac{1}{x}+\frac{1}{y}+\frac{1}{z}=?$ I really am stumped on this problem. I squared the first equation and found that $-y = \sqrt{(x+y)(y+z)}$. So ...
19
votes
8answers
2k views

How does the exponent of a function effect the result?

The $x^{2/2}$ can be represented by these ways: $$\begin{align} x^{2\over2}=\sqrt{x^2} = |x|\\ \end{align} $$ And $$\begin{align} x^{2\over2}=x^{1} = x\\ \end{align} $$ Which one is correct? And what ...
0
votes
3answers
59 views

Intricate exponential equation

This is the question: $$ \frac{(2^{3n+4})(8^{2n})(4^{n+1})}{(2^{n+5})(4^{8+n})} = 2 $$ I've tried several times but I can't get the answer by working out.I know $n =2$, can someone please give me some ...
0
votes
1answer
19 views

Simplify this indices?

Simplify this: $6a^3 * {a^{-5}\over2}$ I got $6a^3 * {1\over2a^5}$ What should I do next? please explain with steps.
41
votes
9answers
2k views

What is exponentiation?

Is there an intuitive definition of exponentiation? In elementary school, we learned that $$ a^b = a \cdot a \cdot a \cdot a \cdots (b\ \textrm{ times}) $$ where $b$ is an integer. Then later on ...
2
votes
7answers
116 views

for $n$ an integer, why is $n^0=1$ ??

This is so going to cost me.... I was wondering why for any integer $n$: $n^0 =1$. Perhaps It's because $n$ is a round number and if $m$ is a non negative integer, also round then: $$n^m = 1 \cdot ...
2
votes
2answers
335 views

Exponent rule and square roots?

For some $x$, $\sqrt{x^2} = |x|$ However, for $x= -1$. $\sqrt{(-1)^2} = (-1^2)^{1/2} = (-1)^{2/2} = (-1)^1 = -1$ Isn't this paradoxical?
5
votes
2answers
107 views

Prove that $\sqrt{8}=1+\dfrac34+\dfrac{3\cdot5}{4\cdot8}+\dfrac{3\cdot5\cdot7}{4\cdot8\cdot12}+\ldots$

Prove that $\sqrt{8}=1+\dfrac34+\dfrac{3\cdot5}{4\cdot8}+\dfrac{3\cdot5\cdot7}{4\cdot8\cdot12}+\ldots$ My work: $\sqrt8=\bigg(1-\dfrac12\bigg)^{-\frac32}$ Now, I suppose there is some "binomial ...
0
votes
3answers
49 views

How do I compute the individual terms of a polynomial to the power of -1?

If my polynomial $p$ is: $x+1$, obviously $p^{-1} = \frac{1}{x+1}$. Is it possible for me to split $\frac{1}{x+1}$ into a sum of two terms? In other words, is there an algorithm to write $p^{-1}$ as ...
0
votes
3answers
60 views

Logarithm properties doubt

The problem is $\log (5.64)^4$. According to the properties and laws of exponents, $\log (m^r) = r \log (m)$. But since the exponent is outside of the parenthesis in this problem, does it solves by ...
0
votes
4answers
69 views

How to compute the exponent?

So I have $a^n = b$. When I know $a$ and $b$, how can I find $n$? Thanks in advance!
2
votes
2answers
78 views

Solution for $4^{2x+1}-3^{3x+1}=4^{2x+3}-3^{3x+2}$

Im trying to get a solution for: $4^{2x+1}-3^{3x+1}=4^{2x+3}-3^{3x+2}$ My main problem is thati dont now how to combine this potencys! Ive also thought about another function that would bring me ...
0
votes
1answer
82 views

Exponential equation+derivative

I saw here on math.stackexchange.com an equation which has very nice solutions (by solutions I mean a proof): $3^x+28^x=8^x+27^x$, where $x$ is a real number. However, I think there must be an ...
1
vote
1answer
84 views

Find $x$ in $\large \,\, A^{A^{{{A^.}^.}^.}}= \,\,(\sqrt [x\cdot x\cdot x\cdot …] x)^{ (((1\cdot x+1)x +1)x +1)x+1…} $

If $\large \,\, A^{A^{{{A^.}^.}^.}}= \,\,(\sqrt [x\cdot x\cdot x\cdot ...] x)^{ (((1\cdot x+1)x +1)x +1)x+1...} $, and $\large \,\,A = (\sqrt[3]{3\sqrt 3 })^{\frac{\sqrt 3}{3}} $, find $x$ I have ...
-3
votes
1answer
75 views
0
votes
4answers
82 views

Calculate approximately the expression $A = 5^{1/2} . 5^{1/4} . 5^{1/8}…$

Calculate approximately the expression $A = 5^{1/2} \cdot 5^{1/4} \cdot 5^{1/8}\cdot\ldots$ My books says to says to do this: $ 5^{1/4} \cdot 5^{1/8} \cdot 5^{1/16}\cdot\ldots = A $ Then $ A = ...
2
votes
2answers
85 views

Definitive answer to existence of real exponents

Well, I've been searching through this fórum and I know this question has been answered many times. But the answers I see, are kinda circular (I think). Let's start by the natural case. Natural case ...
0
votes
1answer
35 views

Prove that $\forall \, a,b \in \mathbb{N}- \{0,1\}\,\, \wedge \,\,a<b \,\, ; \,\, a^{1/a} > b^{1/b}$

Prove that $\forall \, a,b \in \mathbb{N}- \{0,1\}\,\, \wedge \,\,a<b \,\, ; $ $$\,\, a^{1/a} > b^{1/b}$$ I need some tip to start it. Thank you.
3
votes
4answers
98 views

Calculating $\log_7 125$

So the problem asks to calculate $\log_7 125$. It's multiple choice and the options are $2.48$ $4.75$ $1.77$ $2.09$ Given that $7^2 = 49$ and $7^3 = 343$, the answer must be either option 1 or 4, ...
1
vote
3answers
52 views

Exponential Equations

I solved this , but I am not sure if I did in the right way. $$2^{2x + 1} - 2^{x + 2} + 8 = 0$$ $$2^{x + 2} - 2^{2x + 2} = 8$$ $$\log_22^{x + 2} - \log_22^{2x + 2} = \log_28$$ $$x + 2- 2x - 2 = ...
1
vote
1answer
48 views

Simplify an expression.

Don't know how to do this. Simplify the expression, show steps: $$\large \dfrac {a^{-\frac 14}a^{\frac 32}}{a^{\frac 13}}$$ Write the answer using only positive exponents. Assume that all variables ...
1
vote
2answers
44 views

Solve $3^{1/4} \cdot 9^{-5/8}$

I don't understand how to solve $3^{1/4} \cdot 9^{-5/8}$. Help please? I have tried many different things, but they're not working. Once I plug the problem into a math equation solver, the answer ...
0
votes
1answer
414 views

variable with negative exponent in the denominator moved to nominator and vice versa

The top and bottom of the fraction both contain negative exponents. Since $c^{-3}$ on the bottom has a negative exponent, it is moved to the top of the fraction (numerator). Since the $d^{-3}$ on the ...
0
votes
2answers
131 views

How to find $x^4+y^4+z^4$ from equation?

Please help me. There are equations: $x+y+z=3, x^2+y^2+z^2=5$ and $x^3+y^3+z^3=7$. The question: what is the result of $x^4+y^4+z^4$? Ive tried to merge the equation and result in desperado. :( ...
2
votes
1answer
71 views

Trouble solving polynomial equation with exponent

I'm having trouble solving this equation.It looks simple, but I just can't find the answer.Can someone help me? $$9x^4-13x^2+4 = 0$$
0
votes
1answer
29 views

Question about basic exponential/logarithm properties

Solve for $k$: $$e^{k/2}=a$$ Solution: $$e^{2k}=a$$ $$ k/2 = \mathbf{ln}a$$ $$ k=2\mathbf{ln}a$$ $$= \mathbf{ln}a^2$$ My question is: why does $2\mathbf{ln}a = \mathbf{ln}a^2$? Why can you ...
0
votes
1answer
103 views

How to solve $5^n - 5^{n-3} = 5^{n-3} *124$

how is $$5^n - 5^{n-3} = 5^{n-3} *124$$ Can anybody provide a step by step solution.I will greatly appreciate if any online source for such material is provided. Regards
0
votes
1answer
90 views

Solve $a=x^n$ , $b=(x+1)^n$ for $x,n$

$$a=x^n~,~b=(x+1)^n$$ Just trying to solve these for $x$ and $n$ . For some reason WolframAlpha gives me a blank screen? Much thanks for any help.
1
vote
2answers
71 views

Math question from the GMATprep

If $xy=1$ what is the value of: $2^{(x+y)^2}/2^{(x-y)^2}$ A 1 B 2 C 4 D 16 E 19 $(x+y)^2/(x-y)^2$ because $2$ just cancels out from numerator and denominator, ...
2
votes
1answer
95 views

Solve a system of equations with $3$ unknown powers?

I'm trying to solve this, knowing $X$ $$\begin{cases}1^x*2^y*3^z=X\\x+y+z=13\end{cases}$$ So for example, if $X=2048$ , we have $$x=2\\y=11\\z=0$$ I barely have memories from high school ...
2
votes
1answer
106 views

The domain of fractional exponents

Take the following: $$f(x) = x^{6/4}$$ The domain of this function is all real numbers. This function can be simplified to: $$f(x) = x^{3/2}$$ The domain of this function is all real numbers ...
3
votes
3answers
72 views

Can a fourth-order equation be solved like a quadratic equation?

I was asked to find the zeros of $y = x^4 + 5x^2 +6$. I tried to turn this into a quadratic to factor it as follows: $y = x^4 + 5x^2 +6 = {(x^2)}^2 + 5{(x^2)}^1 + 6$ Put another way: Let $t = ...
2
votes
4answers
209 views

How to find $\sqrt{1+{4\over x}+{4\over x^2} }$?

If $$abx^2 = (a-b)^2(x+1)$$ then what is $$\sqrt{1+{4\over x}+{4\over x^2} }$$ (A) $a+b \over a-b$ (B)$a-b\over a+b$ (C) $a^2+ab$ (d) None EDIT: What I've done is this: ...
1
vote
2answers
116 views

Exponential equation with absolute value: $9^{|3x-1|}=3^{8x-2}$

$$9^{|3x-1|}=3^{8x-2}$$ Can someone show me the steps on how to solve this, i've been trying for 30 minutes
-1
votes
1answer
54 views

How do I simplify this expression?

How do I simplify this expression? $$\frac{(4-x)^2 (1/3) (6x+1)^{-2/3} (6) - (6x+1)^{1/3} (-2x)}{(4-x^2)^2}$$
0
votes
1answer
86 views

How do I simplify the expression (a^-1 + b^-1) ^-1?

How do I simplify the expression ... $$(a^{-1} + b^{-1}) ^{-1}$$ ?
0
votes
1answer
34 views

Simplifying exponentials of the form $\,a^x \cdot b^y$

I am given the exponential $\left(\dfrac{1}{2}\right)^x\cdot 4^{(x/2)}$. While my intuition screams that this can be simplified to $\dfrac{2^x}{2^x} = 1$, I am unable to see a concrete mathematical ...
0
votes
1answer
126 views

Simplify the following expressions using fractional exponents

Simplify the following expressions using fractional exponents. Display your answer using fractional exponents. $${ \sqrt[ 3 ]{x^{ 7 }} = }\text{ and }{ \sqrt[ 7 ]{x^{ 3 }} = }$$ Thanks..not sure ...
0
votes
0answers
26 views

How can I go from add a multiplier to an exponent then mod?

If I have a value A, defined as (g^y)%p, and I want to find B, defined as (g^(yc))%p, is the an easy way to figure it out without knowing y (but knowing g,p,c)? I believe that if I had g^y, and I ...
1
vote
1answer
81 views

Systems of equations question

\begin{align*}a^a\cdot b^b\cdot c^c\cdot d^d&=\frac12\\a+b+c+d&=1\end{align*} How can we find solutions for this system of equations given that $a, b, c, d > 0$ ?
9
votes
1answer
401 views

What is wrong with this funny proof that 2 = 4 using infinite exponentiation?

Out of boredom, I decided to recall the following equation: $$x^{x^{x\cdots}} = 2.$$ Which, I simply rewrote like this: $x^2 = 2$, and therefore $x = \sqrt{2}$. Then I took a look at the more ...
1
vote
4answers
64 views

Exponential algebra problem

We need to solve for x: $$54\cdot 2^{2x}=72^x\cdot\sqrt{0.5}$$ My proposed solution is below.
1
vote
2answers
111 views

Multiplying and simplifying expressions

The expression is: $$\frac{24a^4b^2c^3}{25xy^2z^5} \cdot \frac{15x^3y^3z^3}{16a^2b^2c^2}$$ What I did was subtract the exponents of the numerator to the exponents of the denominator. I did a cross ...
3
votes
3answers
109 views

Finding roots of $-3x^{1.25}-3x+10$

I'm in a math workshop, where one of the problems given was $y=–3x^{1.25} –3x+10$. Much to my frustration, the only stated way to find roots was finding x by trial and error. Is there any way to ...
0
votes
2answers
85 views

What is power of number like (power of 2, power of 10)? and how to calculate power of number.

I know my question is very simple to somebody, but I'm still don't understand so far. And now my questions about this subject is: ...
5
votes
2answers
201 views

Suggestions on how to prove the following equality. $a^{m+n}=a^m a^n$

Let $a$ be a nonzero number and $m$ and $n$ be integers. Prove the following equality: $a^{m+n}=a^{m}a^{n}$ I'm not really sure what direction to go in. I'm not sure if I need to show for $n$ ...
3
votes
2answers
61 views

Proving that not defined value is equal to something

My younger brother (9th Grader) got the following maths problem- Given: $$2^a = 3^b = 6^c$$ Prove: $$c=\frac{a * b}{a+b}$$ From my elementary knowledge of mathematics it seems like a=b=c=0.Also, ...
5
votes
3answers
382 views

Solve an equation with $e^{(x-2)}=e^{4}\cdot e^{\sqrt{x}}$

$$e^{(x-2)}=e^{4}e^\sqrt{x}$$ I know that $x = 9$ and I can show the calculations like this: $$e^{(x-2)} = e^{\sqrt{x}+4}$$ and now I need to get the $x$ to the right side but I dont know how.
0
votes
3answers
73 views

Which of the folowing no. is largest [closed]

Which of the folowing no. is largest-- $2^{3^{4}}$ , $2^{4^{3}}$ , $3^{2^{4}}$ , $3^{4^{2}}$ , $4^{2^{3}}$ , $4^{3^{2}}$. I am stuck on this problem. Can anyone help me please...