1)) Simplify. Assume all variables are positive. \( d^{\frac{1}{7}} \div d^{\frac{5}{7}} \) Write your answer in the form \( A \) or \( \frac{A}{B^{\prime}} \), where \( A \) and \( B \) are expressions that have no variables in common. All exponents Dositive

To simplify the expression \( d^{\frac{1}{7}} \div d^{\frac{5}{7}} \), follow these steps: 1. **Apply the Law of Exponents for Division**: When dividing powers with the same base, subtract the exponents: \[ d^{\frac{1}{7}} \div d^{\frac{5}{7}} = d^{\frac{1}{7} - \frac{5}{7}} = d^{-\frac{4}{7}} \] 2. **Express with Positive Exponents**: Since all exponents should be positive, rewrite \( d^{-\frac{4}{7}} \) as: \[ \frac{1}{d^{\frac{4}{7}}} \] Therefore, the simplified form of the expression is: \[ \boxed{\dfrac{1}{d^{4/7}}} \]