Algebra: Using Special Symbols

1. Let $x$ § $y = x ^y +y$ for all positive integers of $x$ and $y$. What is the value of $4$ § $2$?

(A) 20

(B) 18

(C) 16

(D) 22

(E) 24

2. ¤ • 2 + 8 ÷ 4 = 34

What number when used in place of ¤ above, makes the statement true?

(A) 16

(B) 28

(C) 42

(D) 60

(E) 64

3. Let $a$ Ω $b$ = $(-2a)^3 + b^2$ for all positive integers $a$ and $b$.

State the value of $3$ Ω $12$.

(A) 360

(B) -360

(C) 72

(D) -72

(E) -198

4. Let $x$ ♠ $y$ ♠ $z$ = 5 ($x$ + $z$) - $y^2$ for all positive integers of $x$, $y$, and $z$. What is the value of 7 ♠ 8 ♠ 9?