1)) Simplify. Assume all variables are positive. \( r^{\frac{7}{5}} \div r^{\frac{14}{5}} \) ()) Write your answer in the form \( A \) or \( \frac{A}{B^{\prime}} \) where \( A \) and \( B \) expressions that have no variables in common. All expone

To simplify \( r^{\frac{7}{5}} \div r^{\frac{14}{5}} \), we can use the property of exponents that states \( a^{m} \div a^{n} = a^{m-n} \). Applying this here gives us: \[ r^{\frac{7}{5} - \frac{14}{5}} = r^{\frac{7 - 14}{5}} = r^{-\frac{7}{5}} \] This can be rewritten as: \[ \frac{1}{r^{\frac{7}{5}}} \] So our answer is \( \frac{1}{r^{\frac{7}{5}}} \). Additionally, diving into the world of exponent rules can be incredibly useful. Remember that negative exponents indicate reciprocals, which is an elegant way to express division in terms of multiplication. Knowing how to manipulate these can simplify many algebraic expressions rapidly! When working with exponents, a common mistake is misapplying the exponent rules, especially with negative exponents or forgetting to combine the exponents correctly. Take your time to double-check your calculations, especially during subtraction in the exponent!