Simplify:
$\left(1^{3}+2^{3}+3^{3}\right)^{\frac{1}{2}}$
If $a=\frac{3+\sqrt{5}}{2},$ then find the value of $a^{2}+\frac{1}{a^{2}}$.
State whether each of the following statements is true or false
$(-5)^{2}=-25$
Express $0 . \overline{83}$ in the form $\frac{p}{q} ;$ where $p$ and $q$ are integers and $q \neq 0$.
Express $1.23 \overline{4}$ in the form $\frac{p}{q} ;$ where $p$ and $q$ are integers and $q \neq 0$
If $125^{x}=\frac{25}{5^{x}},$ then find the value of $x$.