\(697:\left[\left(15y+52\right):2\right]=17\)
=>\(\dfrac{15y+52}{2}=\dfrac{697}{17}=41\)
=>15y+52=82
=>15y=30
=>y=2
\(5^{x-2}-3^2=2^4-\left(2^8\cdot2^4-2^{10}\cdot2^2\right)\)
=>\(5^{x-2}-9=16-\left(2^{12}-2^{12}\right)=16\)
=>\(5^{x-2}=9+16=25=5^2\)
=>x-2=2
=>x=4
\(x\cdot y=4\cdot2=8\)