Simplify $\dfrac{x^{8}}{x^{3}}$ for $x \ne 0$.

Apply the quotient rule for exponents: $\dfrac{x^{a}}{x^{b}} = x^{a - b}$. $\dfrac{x^{8}}{x^{3}} = x^{8 - 3} = x^{5}$. - Trap B ($x^{11}$) adds exponents (product rule misused for quotient). - Trap C ($x^{8/3}$) divides exponents — wrong operation. - Trap D ($x^{24}$) multiplies exponents (power rule misused). Mnemonic: the four basic exponent operations — *same base*: - Product: $x^{a} \cdot x^{b} = x^{a+b}$ — exponents **add**. - Quotient: $\dfrac{x^{a}}{x^{b}} = x^{a-b}$ — exponents **subtract**. - Power: $(x^{a})^{b} = x^{ab}$ — exponents **multiply**. - Roots: $\sqrt[n]{x^{a}} = x^{a/n}$ — exponents **divide**.