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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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Why does the rule say that,if a^x=a^y,when a is greater than 0 and a is not equal to 1?what if a were less than 0?

I am an 6th grade student.And just learning the rules of exponents . Please don't close the question.An explanation would be appreciable and I'll be very great full if the question is answered.
user459284
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How to combine $5*3^{(x+1)}$

I came across the following equality: $$\frac{2^x}{5*3^{(x+1)}}=\frac1{15}\left(\frac23\right)^x$$ Why is this? More specifically, what I don't understand is how to combine the $5*3^{(x+1)}$.
Burt
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What does this rule mean?

I read this rule in a book .it says, If $a>0$, $a$ is not equal to $1$ and $a^x=a^y$,then $x=y$. But I don't understand why the value of $a$ has to be greater than $0$. What if the value of $a$ was less than $0$? Wouldn't it be the same ?For…
user459284
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Can the product of two expressions(exponents of different base and power) be reduced into one expression of one base and power?

Suppose you have the product of two expressions: $ 2^5$ * $ 2^2$, the result will be : $ 2^{5+2}$ = $ 2^7$. This is because we know the exponent rule that if they have the same base, we can add the power. Is there a way to express the product of two…
Monolica
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I have a simple problem which gives two different solutions in two different calculators.

I hope that this kind of questions doesn't break the site's rules. I have this simple problem which gives two different solutions in two different calculators (Wolfram Alpha and Symbolab). What am I doing wrong in the calculation…
Brian Díaz Flores
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A question on Greek letters used for math

The Greek letter sigma is used for repeated addition. The Greek letter pi( uppercase, not lowercase), is used to denote repeated multiplication. In the same way as the last two, which symbol is used to show repeated exponentiation? (Notice: I…
elipson_-1
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A question about Exponents

I've been reading about Exponents, and I was wondering if there is a shorter way to do this same calculation, below: 24 = 2 * 2 * 2 * 2 = 16 I keep seeing what seems to me a pattern in this, and other examples. The pattern I keep seeing (maybe…
Tommy
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Addition with variable in exponent

I know that $2^x$+$2^x$=$2^{x+1}$ but I can not explain why. Googling returns too much information about the situation involving variable in the base. Can someone explain? A link to a reference would be sufficient. Thanks
Max Wen
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A problem in algebra: how does $-1=1$?

I have algebra problem from a friend, that is 1=-1!!! because $$-1=-1^{3}=-1^{^{\frac{6}{2}}}=\sqrt{(-1)^6}=\sqrt{1}=1$$ I can not see what is wrong with this? I will appreciate it any help.
Ahmed
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Is there a shorter way to say "b raised to the n-th power"

$b^n$ Alternatives that I know are correct: "b raised to the power of n" "the n-th power of b" Can I just say "b raised to n" or "b to n" or are these technically wrong?
Niko Bellic
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Why is $a^{-x}$ defined to be equal to $\frac{1}{a^x}$?

I have searched the reason behind this definition in two textbooks and haven't found any. They just state that this is the definition but don't ever give any motivation for why this is truth. Edit: I figured out why that relation must be true about…
Sigma
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${x^4}$ as "tesseracting" a number $x$

So, this strange thought popped up into my head. You know how we call ${x^2}$ squaring due to the fact that what you're essentially doing is finding the area of a square with side length $x$? The same goes for cubing. Saying ${x^3}$ is really going…
Xavier Stanton
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Proof of exponentiation law

I want to prove this : $(ab)^n = a^nb^n$ with a, b and n real numbers. I know how to prove this when n is an integer but not when n is a real number. I really don't know where to start to prove this. Can you help me ? Thank you.
Never
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Why are negative exponents dividing instead of multiplying?

In trying to relearn scientific notation after years since I left school, I noticed that when we get a very small number and convert it to scientific notation, you're actually multiplying the tiny number a certain number of times so that the number…
Ezequiel Barbosa
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Is the 4th root of $3^3$ $3^3/4$ or $2.2795$?

I'm working through a textbook and one question is: Use a calculator to find the value of the following expression: $$\sqrt[\large4]{3^3}$$ The textbook answer is given as $2.2795$; however, using https://live.sympy.org/, if I enter root(3**3, 4),…
Doug Fir
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