\(63^{15}< 64^{15}=\left(2^6\right)^{15}=2^{90}=\left(2^5\right)^{18}=32^{18}< 34^{18}\)
\(63^{15}=\left(63^5\right)^3=992436543^3\)
\(34^{18}=\left(34^6\right)^3=1544804416^3\)
\(992436543< 1544804416\Rightarrow992436543^3< 1544804416^3\)
\(\Rightarrow63^{15}< 34^{18}\)