$$$$ are not as simple

Observe, first equation is of the form, $x \$y = x×(y+1)$
Second equation is of the form, $x \$y= x×(y+2)$
Third equation is of the form, $x \$y= x×(y+3)$
Fourth equation is of the form, $x \$y= x×(y+4)$
Fifth equation is of the form, $x \$y= x×(y+5)$
Then, sixth equation is of the form $x \$y = x×(y+6)$ = $7×(8+6)$ = $7×14$ = $98$ . $_\square$

Notice that $n\$m = n\times m + n\times (n - 1)$ Substitute $n = 7$ and $m = 8$ to get $56 + 42 = \boxed{98}$

On a little analysis,

$n\$m\quad =\quad n*(n+m-1)$

So,

$7\$8\quad =\quad 7*(7+8-1)\\ \quad \quad \quad \quad =\quad 98$

2+3=2*[3+(2-1)]=8

3+7=3*[7+(3-1)]=27

4+5=4*[5+(4-1)]=32

5+8=5*[8+(5-1)]=60

6+7=6*[7+(6-1)]=72

therefore

7+8=7*[8+(7-1)]=98

x+y=x[y+(x-1)]=x^2+xy-x