Answer
2
Work Step by Step
Based on the power rule for exponents, we know that $(a^{m})^{n}=a^{mn}$ (where $m$ and $n$ are positive integers and $a$ is a real number).
Therefore, $(5^{0})^{3}+(y^{0})^{7}=5^{0\times3}+y^{0\times7}=5^{0}+y^{0}=1+1=2$.
Recall that any nonzero real number raised to the power of zero will have a value of 1.