Question
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
Ask by Ramirez Sherman. in the United States
Jan 23,2025
Real Tutor Solution
Tutor-Verified Answer
Answer
\[
\frac{1}{d^{\frac{4}{7}}}
\]
Solution
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:
\[
\boxed{\dfrac{1}{d^{4/7}}}
\]
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Simplify this solution The Deep Dive
To simplify \( d^{\frac{1}{7}} \div d^{\frac{5}{7}} \), you subtract the exponents since you are dividing the same base: \[ d^{\frac{1}{7} - \frac{5}{7}} = d^{\frac{1 - 5}{7}} = d^{\frac{-4}{7}}. \] Now, to express it in the required form, we write \( d^{\frac{-4}{7}} \) as: \[ \frac{1}{d^{\frac{4}{7}}}. \] So, the final simplified form is: \[ \frac{1}{d^{\frac{4}{7}}}. \]
