Problem 170
Prove that \(\displaystyle (a^{x})^{y}=a^{xy}\) if \(\displaystyle a>0\) and \(\displaystyle x,y\in \Q\). Difficulty: 6. |
Problem 171
Prove that \(\displaystyle (1+x)^{r}\leq 1+rx\) if \(\displaystyle r\in\Q\), \(\displaystyle 0<r<1\) and \(\displaystyle x\geq -1\). Difficulty: 6. Solution is available for this problem. |
Problem 172
Can \(\displaystyle x^y\) be (ir)rational if \(\displaystyle x\) is (ir)rational and \(\displaystyle y\) is (ir)rational (these are 8 exercises)? Difficulty: 6. |
Supported by the Higher Education Restructuring Fund allocated to ELTE by the Hungarian Government |