Question

simplify.
\\(\frac{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

When dividing like bases, subtract exponents: $\frac{w^a}{w^b}=w^{a-b}$
So we get $w^{\frac{1}{3}-\frac{7}{9}}$

Step2: Subtract the fractions

Find a common denominator (9) for the exponents:
$\frac{1}{3}-\frac{7}{9}=\frac{3}{9}-\frac{7}{9}=-\frac{4}{9}$
Result: $w^{-\frac{4}{9}}$

Step3: Rewrite with positive exponent

Use the rule $w^{-n}=\frac{1}{w^n}$ to eliminate the negative exponent:
$\frac{1}{w^{\frac{4}{9}}}$

Answer:

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