1. Problem: Find the factors of $11x^2y$. Factors are numbers or variables multiplied together to get the expression. Here, the factors are $11$, $x$, $x$, and $y$. 2. Problem: Write $5(d)(d)(d)(z)(z)$ using exponents. Using exponent rules, repeated multiplication of the same base is written as powers. So, $5d^3z^2$. 3. Problem: What is $w^0$ equal to? Any nonzero number raised to the zero power equals 1. So, $w^0 = 1$. 4. Problem: Write the product of "x and y" as an algebraic expression. The product means multiplication, so the expression is $xy$. 5. Problem: Write "a increased by 12" as an algebraic expression. This means $a + 12$. 6. Problem: Write "the difference of 7 and 9" as an algebraic expression. Difference means subtraction, so $7 - 9$. 7. Problem: If $a=3$ and $b=-2$, evaluate $3a - 5ab + b^2$. Step 1: Substitute values: $3(3) - 5(3)(-2) + (-2)^2$ Step 2: Calculate each term: $9 - 5(3)(-2) + 4$ Step 3: Calculate $-5(3)(-2) = -5 imes 3 imes -2 = 30$ Step 4: So expression is $9 + 30 + 4$ Step 5: Sum: $9 + 30 + 4 = 43$ 8. Problem: If $m=-5$ and $w=4$, evaluate $mw - 4m - (3 + w)$. Step 1: Substitute values: $(-5)(4) - 4(-5) - (3 + 4)$ Step 2: Calculate each term: $-20 + 20 - 7$ Step 3: Sum: $-20 + 20 - 7 = -7$ Final answers: 1. Factors: $11$, $x$, $x$, $y$ 2. $5d^3z^2$ 3. $1$ 4. $xy$ 5. $a + 12$ 6. $7 - 9$ 7. $43$ 8. $-7$