1. **State the problem:** Simplify the expression $5p^0 + (7p)^0$. 2. **Recall the rule:** Any nonzero number raised to the power of 0 is 1, i.e., $a^0 = 1$ for $a \neq 0$. 3. **Apply the rule:** - $p^0 = 1$ since $p \neq 0$. - $(7p)^0 = 1$ since $7p \neq 0$. 4. **Substitute these values back into the expression:** $$5p^0 + (7p)^0 = 5 \times 1 + 1 = 5 + 1$$ 5. **Simplify the sum:** $$5 + 1 = 6$$ **Final answer:** $6$