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Any interval $[s,2s]$ contains power of $2$

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#inequality #exponentiation
224
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Why can't we separate fraction powers in euler's formula?

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#complex-numbers #exponentiation #fractions
193
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Why does $x^{\frac{1}{a}} = \sqrt[a]{x}$?

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#exponentiation #radicals
56
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Restriction when use $a^{p/q}=(a^{1/q})^{p}$

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#exponentiation
231
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Solving equation with 2 variables without bruteforce

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#number-theory #logarithms #diophantine-equations #exponentiation
240
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How can $(2^{100}-2^{98})(2^{99}-2^{97})$ be written in terms of its prime factors?

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#algebra-precalculus #exponentiation #prime-factorization
38
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Is it possible to prove $\exists x. a^x = b$ without logarithms?

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#logarithms #exponentiation
101
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sum of $p^{\text{th}}$ powers of a set of $n$ variables $x_i$

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#exponentiation #approximation
100
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Prove that if $n < m$ with $n,m \in \mathbf{Z}$ and $x>1$, then $x^n < x^m$.

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#induction #exponentiation #real-numbers
236
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How would one solve the equation $2^x=x^3-1$?

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#exponentiation #lambert-w
76
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Proof that N to the power 0 is 1 using square roots

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#proof-verification #exponentiation #alternative-proof
213
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Odd powers with a negative base

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#exponentiation
315
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What is the result of $2^{{2}^{{2}^{{2}^{0}}}}$?

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#algebra-precalculus #exponentiation
315
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What does $2^{2.5}$ mean

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#exponentiation #fractions
54
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Tools for determining the "central" digits of large integer powers (or lack thereof)?

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#number-theory #elementary-number-theory #exponentiation #integers #decimal-expansion

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