Let \( a=5^{-1}\cdot\sqrt5 \), \( b=5^{-\frac32}\cdot25 \), \( c=125^{\frac14}:5^{-3} \), \( d=5^{\frac13}\cdot25^{-\frac13} \). Which of these numbers is the biggest?
Let \( a=\left(\frac23\right)^{\sqrt7-\sqrt3} \) and \( b=\left(\frac23\right)^{\sqrt3+2} \).
Which of the following relations is true for \( a \) and \( b \)?
Writing the expression \( \frac{\sqrt[3]3\cdot9\cdot\sqrt{27}\cdot\sqrt[6]{81}}{81\cdot\sqrt[3]{\frac13}\cdot\sqrt[4]9} \) in the form of a power of \( 3 \), we will get: