Question

simplify.
\\(\dfrac{w^{\frac{1}{3}}}{w^{\frac{7}{9}}}\\)
write your answer using only a positive exponent.
assume that the variable represents a positive real number.

Explanation:

Step1: Apply exponent quotient rule

$\frac{w^{\frac{1}{3}}}{w^{\frac{7}{9}}} = w^{\frac{1}{3} - \frac{7}{9}}$

Step2: Subtract the fractions

$\frac{1}{3} - \frac{7}{9} = \frac{3}{9} - \frac{7}{9} = -\frac{4}{9}$

Step3: Convert to positive exponent

$w^{-\frac{4}{9}} = \frac{1}{w^{\frac{4}{9}}}$

Answer:

$\frac{1}{w^{\frac{4}{9}}}$