Question

simplify. assume all variables are positive.\\(\frac{w^{\frac{3}{4}}}{w^{\frac{9}{4}}}\\)\
write your answer in the form \\(a\\) or \\(\frac{a}{b}\\), where \\(a\\) and \\(b\\) are constants or variable expressions that have no variables in common. all exponents in your answer should be positive.

Explanation:

Step1: Apply exponent division rule

When dividing terms with the same base, subtract exponents: $\frac{w^m}{w^n}=w^{m-n}$
$\frac{w^{\frac{3}{4}}}{w^{\frac{9}{4}}}=w^{\frac{3}{4}-\frac{9}{4}}$

Step2: Calculate the exponent

Subtract the fractions in the exponent.
$w^{\frac{3-9}{4}}=w^{-\frac{6}{4}}$

Step3: Simplify the exponent

Reduce the fraction and rewrite negative exponent as positive.
$w^{-\frac{3}{2}}=\frac{1}{w^{\frac{3}{2}}}$

Answer:

$\frac{1}{w^{\frac{3}{2}}}$