Exponentiation with infix operators in or operating on the base

In Raku by default, infix exponentiation binds tighter than unary negation. It is trivial however to define your own infix operators with whatever precedence level meets the needs of your program.

A slight departure from the task specs. Use 1 + {expression} rather than just {expression} to better demonstrate the relative precedence levels. Where {expression} is one of:

Also add a different grouping: (1 + -x){exponential operator}p

sub infix:<↑> is looser(&prefix:<->) { $^a ** $^b }
sub infix:<∧> is looser(&infix:<->)  { $^a ** $^b }

for
   ('Default precedence: infix exponentiation is tighter (higher) precedence than unary negation.',
     '1 + -$x**$p',   {1 + -$^a**$^b},   '1 + (-$x)**$p', {1 + (-$^a)**$^b},  '1 + (-($x)**$p)', {1 + (-($^a)**$^b)},
     '(1 + -$x)**$p', {(1 + -$^a)**$^b}, '1 + -($x**$p)', {1 + -($^a**$^b)}),

   ("\nEasily modified: custom loose infix exponentiation is looser (lower) precedence than unary negation.",
     '1 + -$x↑$p ',   {1 + -$^a↑$^b},    '1 + (-$x)↑$p ', {1 + (-$^a)↑$^b},   '1 + (-($x)↑$p) ', {1 + (-($^a)↑$^b)},
     '(1 + -$x)↑$p ', {(1 + -$^a)↑$^b},  '1 + -($x↑$p) ', {1 + -($^a↑$^b)}),

   ("\nEven more so: custom looser infix exponentiation is looser (lower) precedence than infix subtraction.",
     '1 + -$x∧$p ',   {1 + -$^a∧$^b},    '1 + (-$x)∧$p ', {1 + (-$^a)∧$^b},   '1 + (-($x)∧$p) ', {1 + (-($^a)∧$^b)},
     '(1 + -$x)∧$p ', {(1 + -$^a)∧$^b},  '1 + -($x∧$p) ', {1 + -($^a∧$^b)})
-> $case {
    my ($title, @operations) = $case<>;
    say $title;
    for -5, 5 X 2, 3 -> ($x, $p) {
        printf "x = %2d  p = %d", $x, $p;
        for @operations -> $label, &code { print " │ $label = " ~ $x.&code($p).fmt('%4d') }
        say ''
    }
}

Output:

Default precedence: infix exponentiation is tighter (higher) precedence than unary negation.
x = -5  p = 2 │ 1 + -$x**$p =  -24 │ 1 + (-$x)**$p =   26 │ 1 + (-($x)**$p) =  -24 │ (1 + -$x)**$p =   36 │ 1 + -($x**$p) =  -24
x = -5  p = 3 │ 1 + -$x**$p =  126 │ 1 + (-$x)**$p =  126 │ 1 + (-($x)**$p) =  126 │ (1 + -$x)**$p =  216 │ 1 + -($x**$p) =  126
x =  5  p = 2 │ 1 + -$x**$p =  -24 │ 1 + (-$x)**$p =   26 │ 1 + (-($x)**$p) =  -24 │ (1 + -$x)**$p =   16 │ 1 + -($x**$p) =  -24
x =  5  p = 3 │ 1 + -$x**$p = -124 │ 1 + (-$x)**$p = -124 │ 1 + (-($x)**$p) = -124 │ (1 + -$x)**$p =  -64 │ 1 + -($x**$p) = -124

Easily modified: custom loose infix exponentiation is looser (lower) precedence than unary negation.
x = -5  p = 2 │ 1 + -$x↑$p  =   26 │ 1 + (-$x)↑$p  =   26 │ 1 + (-($x)↑$p)  =   26 │ (1 + -$x)↑$p  =   36 │ 1 + -($x↑$p)  =  -24
x = -5  p = 3 │ 1 + -$x↑$p  =  126 │ 1 + (-$x)↑$p  =  126 │ 1 + (-($x)↑$p)  =  126 │ (1 + -$x)↑$p  =  216 │ 1 + -($x↑$p)  =  126
x =  5  p = 2 │ 1 + -$x↑$p  =   26 │ 1 + (-$x)↑$p  =   26 │ 1 + (-($x)↑$p)  =   26 │ (1 + -$x)↑$p  =   16 │ 1 + -($x↑$p)  =  -24
x =  5  p = 3 │ 1 + -$x↑$p  = -124 │ 1 + (-$x)↑$p  = -124 │ 1 + (-($x)↑$p)  = -124 │ (1 + -$x)↑$p  =  -64 │ 1 + -($x↑$p)  = -124

Even more so: custom looser infix exponentiation is looser (lower) precedence than infix subtraction.
x = -5  p = 2 │ 1 + -$x∧$p  =   36 │ 1 + (-$x)∧$p  =   36 │ 1 + (-($x)∧$p)  =   26 │ (1 + -$x)∧$p  =   36 │ 1 + -($x∧$p)  =  -24
x = -5  p = 3 │ 1 + -$x∧$p  =  216 │ 1 + (-$x)∧$p  =  216 │ 1 + (-($x)∧$p)  =  126 │ (1 + -$x)∧$p  =  216 │ 1 + -($x∧$p)  =  126
x =  5  p = 2 │ 1 + -$x∧$p  =   16 │ 1 + (-$x)∧$p  =   16 │ 1 + (-($x)∧$p)  =   26 │ (1 + -$x)∧$p  =   16 │ 1 + -($x∧$p)  =  -24
x =  5  p = 3 │ 1 + -$x∧$p  =  -64 │ 1 + (-$x)∧$p  =  -64 │ 1 + (-($x)∧$p)  = -124 │ (1 + -$x)∧$p  =  -64 │ 1 + -($x∧$p)  = -124