1. **Problem Statement:** Check the exponent properties and simplifications given in the quiz. 2. **Reviewing each step:** - $5 + 7 = 12$, not 11. So this is incorrect. - $y^5 \cdot y^7 = y^{5+7} = y^{12}$, but the quiz shows $y$, which is incorrect. - $(y^5)^2 = y^{5 \cdot 2} = y^{10}$, this is correct. - $15 \div 3 = 5$, correct. - $15x^2 y^5$ is just an expression, no operation to check. - $3x + y5$ is ambiguous; if it means $3x + y^5$, it's an expression. - $\frac{5}{x^2}$ is correct as written. - $(4x^{3}5 \cdot 3x^{0}y^{2})^{-1}$ simplifies as follows: Step 1: $4 \cdot 5 \cdot 3 = 60$ Step 2: $x^{3} \cdot x^{0} = x^{3+0} = x^{3}$ Step 3: $y^{2}$ So inside parentheses: $60 x^{3} y^{2}$ Taking the inverse: $(60 x^{3} y^{2})^{-1} = \frac{1}{60 x^{3} y^{2}}$ - $\frac{2 x^{5}}{y^{4}}$ is correct. - $x^{-3} = \frac{1}{x^{3}}$, correct. - $2 x^{-3} = 2 \cdot \frac{1}{x^{3}} = \frac{2}{x^{3}}$, correct. - $8 - (-3) = 8 + 3 = 11$, correct. - $12 \div 6 = 2$, correct. - $2 \cdot \frac{m^{8}}{m^{-3}} = 2 m^{8 - (-3)} = 2 m^{11}$, correct. - $\frac{x^{5} \cdot x}{\sqrt{y}} = \frac{x^{5+1}}{y^{1/2}} = \frac{x^{6}}{y^{1/2}}$, but quiz shows $(x^{5} y)/(x^{2} y^{3})$ which is different and seems incorrect. - $-x^{1} 4 x^{-2} y^{-3} = -4 x^{1 - 2} y^{-3} = -4 x^{-1} y^{-3} = -\frac{4}{x y^{3}}$, correct. - $2/x^{3}$ multiplied by $2/x^{3}$ equals $\frac{4}{x^{6}}$, but quiz shows multiplication to get $2/x^{3}$ which is incorrect. - $-\frac{1}{2} x^{5} y^{5} / 2 = -\frac{1}{2} x^{5} y^{5} \cdot \frac{1}{2} = -\frac{1}{4} x^{5} y^{5}$, correct. - Simplifications involving $-2x$ and $4$ over $y$ and $5$ are unclear without exact expressions. 3. **Summary:** - Some arithmetic errors (e.g., $5+7=11$ is wrong). - Exponent rules mostly applied correctly except in the $y^{5} \cdot y^{7}$ case. - Some expressions are ambiguous or incorrectly simplified. 4. **Final note:** Review carefully the addition of exponents when multiplying like bases and arithmetic sums.