Write $(-5)^5\div5^3+3^{4}-6^{1}$ as an integer.
I start with the parentheses, but there is nothing I can do inside them, so I move on to the exponents. I need to evaluate $(-5)^5$, $5^3$, $3^4$, and $6^1$ before I do anything else. I know that a negative number raised to an odd power is still negative, so $(-5)^5=-3125$. I also know that $5^3=125$, $3^4=81$, and $6^1=6$, so I can replace those expressions with their values. Now I have $-3125\div125+81-6$. Next, I do the division, since it has higher precedence than addition and subtraction. I know that $-3125\div125=-25$, so I can replace that expression with its value. Now I have $-25+81-6$. Finally, I do the addition and subtraction, from left to right. I know that $-25+81=56$ and $56-6=50$, so I can simplify the expression to $50$. This is an integer, so I am done. 