Questions tagged [exponentiation]

Questions about exponentiation, the operation of raising a base $b$ to an exponent $a$ to give $b^a$.

3,061 questions
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Subtracting exponents properties?

Background : I was reviewing some practice problems for a small local math competition, and I don't understand how the give solution works. I don't know how this, $$9^{x+2} - 9^x=240$$ is the same ...
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$(-1)^3$ has different results when evaluated as $(-1)\times(-1)\times(-1) = -1$ vs $((-1)^2)^{3/2} = 1$. Which is correct?

I know that $$(-1)^3=(-1)\times(-1)\times(-1)=-1 \tag{1}$$ but also $$(-1)^3=((-1)^2)^{3/2}=1^{3/2}=1 \tag{2}$$ So which gives the correct value of $(-1)^3$?
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A problem in algebra: how does $-1=1$? [duplicate]

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.
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What is the base of this exponent?

Given the following, what is the value of $2b^5$? $$b = 5$$ $$2b^2$$ I'm confused as to whether the exponent applies to $2b$ or just $b$. Thus, does $2b^2$ equal 50 or 100? What is the ...
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How do I solve for $x$ in $ab^x-cd^x=e$?

For example: I know that $5*1.2^{13}-8*1.1^{13}\approx26$. How do I find the exponential value (13 in the previous example) that would equate to 26 exactly? The answer should be something close to 13....
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solve variable in base

I am asking very petty question. I am confused to solve following equation. Answer should be 9.03. When I calculate, I constantly get different answer (696.4). How would you solve? then I wanna know ...
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Why is $a^{-x}$ defined to be equal to $\frac{1}{a^x}$? [duplicate]

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: ...
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If $2^a=3^b$ find $\frac{a}{b}$ [closed]

I tried many different things but still couldn't solve it. Could you please give me a clue?
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Why is $a^x = e^{x \log a}$?

Why is $a^x = e^{x \log a}$, where $a$ is a constant? From my research, I understand that the the natural log of a number is the constant you get when you differentiate the function of that ...
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Proof that $x^{(n+4)} \mod 10 = x^n \mod 10$

While solving a programming challenge in which one should efficiently compute the last digit of $a^b$, I noticed that apparently the following holds (for $n > 0$) $x^{(n+4)} \mod 10 = x^n \mod 10$ ...