"5z squared" can be written as "5z^2" without quotes of course.
The * symbol is used to mean "times"
So "5z squared times 10z" can be written as 5z^2*10z
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The coefficients 5 and 10 multiply to 5*10 = 50
The z terms multiply to z^2*z = z^3
So overall, the simplified answer is 50z^3