In this expression, the 0 exponent is only applied to the z, so z is 1. Exponents only apply to numbers directly next to them, or parentheses directly next to them- in which case it will apply to everything inside the parentheses.
Order of operations : Parentheses Exponents Multiply Divide Add Subtract
1. 4(z0)+7 ----> 4(1) +7
2. Multiply the 4 and 1. So, 4 + 7
3. Add. 4+7=11
Final answer is 11.