The 4 in the symbol is the index of the radical sign √.
Whether you can write this expression on a calculator depends on the calculator... If you have one with a CAS (that is, a "computer algebraic system"), chances are there is a built-in button for things like square roots and cube roots, and possibly roots of higher indices. If not, you can always express a radical expression using a fractional exponent, such as
[tex]\sqrt x\iff x^{\frac12}[/tex]
or
[tex]\sqrt[3]{x}\iff x^{\frac13}[/tex]
or
[tex]\sqrt[4]{x}\iff x^{\frac14}[/tex]
and so on. So the given expression could be typed in as (16*x^6*y^7)^(1/4), for instance.
I'm guessing you have to simplify the given expression. You could end up with
∜(16x ⁶y ⁷) = ∜(2⁴ x ⁴ x ² y ⁴ y ³)
… = 2xy ∜(x ² y ³)
(assuming x and y are positive)
