Question
f. \( \frac{15^{\frac{17}{6}}}{15^{\frac{5}{6}}} \)
Ask by Welch Wheeler. in the United States
Mar 19,2025
Upstudy AI Solution
Tutor-Verified Answer
Answer
Simplify the expression \( 15^{17/6} \div 15^{5/6} \) to \( 15^{(17/6 - 5/6)} = 15^{12/6} = 15^2 = 225 \).
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The Deep Dive
To simplify the expression \( \frac{15^{\frac{17}{6}}}{15^{\frac{5}{6}}} \), we can utilize the properties of exponents. Specifically, when dividing two expressions with the same base, we subtract the exponents. So, we compute: \[ 15^{\frac{17}{6} - \frac{5}{6}} = 15^{\frac{17 - 5}{6}} = 15^{\frac{12}{6}} = 15^{2} \] Thus, the simplified result is: \[ 15^{2} = 225 \] So, \( \frac{15^{\frac{17}{6}}}{15^{\frac{5}{6}}} = 225 \).
