# Tagged Questions

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### From an expression raised in a power of 2 to an expression raised in the power or 10

Is there a simple/"easy" way to convert a big number from a power of $2$ to a power of $10$ equivalent. Example: I had $2^{127}\cdot 1.9999999$ which I did the multiplication got the result and from ...
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### Why is the result of $-2^2 = -4$ but $(-2)^2 =4$?

I am really new into math, why is $-2^2 = -4$ and $(-2)^2 = 4$?
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### Evaluate $\frac{\frac{1}{1}}{\frac{1}{5^{-2}}}$

I solved a question in the Manhattan GRE 5 pound book (specifically the 11th question in the Exponents and Roots section). I evaluated $\frac{\frac{1}{1}}{\frac{1}{5^{-2}}}$ as $5^{-2}$ and then ...
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### Combination of quadratic and arithmetic series

Problem: Calculate $\dfrac{1^2+2^2+3^2+4^2+\cdots+23333330^2}{1+2+3+4+\cdots+23333330}$. Attempt: I know the denominator is arithmetic series and equals ...
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### Why is $\left(1-\frac{1}{k}\right)^t < e^{-t/k}$?

I came across this statement, but can't see why it holds: $\left(1-\frac{1}{k}\right)^t < e^{-t/k}$ I'm sure it's something simple, but I don't have a great deal of mathematical experience. I ...
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### How can you prove that a value raised to a fraction($\frac{1}{2}$ for example), is $\sqrt{x}$?

I know that if you raise a value to $\frac{1}{2}$ for example, you take the square root, but that is not what I am asking, what I am asking is; what are you actually doing when raising a value to ...
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### Two variable integer equation

I have the following equation: $$p^q(2^{q-1}-1)=9p^7q$$ I need to solve for $p$ and $q$. $p$ and $q$ are integers. I think I could take the case $p=0$ separately and for that one $q$ could be ...
Find the value of $(-2)^{-(2)^{(-2)}}$. Is it 16/8/-8/none? My attempt: $a^{-x}=\frac1{a^x}$, so, $(-2)^{-(2)^{(-2)}}=(-2)^{\frac{-1}{2^2}}=\frac{1}{(-2)^{\frac14}}$. That is, I would pick 'none ...