Question

simplify. assume all variables are positive.\\(\frac{x^{\frac{7}{4}}}{x^{\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 subtraction rule

When dividing like bases, subtract exponents: $x^{\frac{7}{4} - \frac{9}{4}}$

Step2: Calculate the exponent

$\frac{7}{4} - \frac{9}{4} = -\frac{2}{4} = -\frac{1}{2}$

Step3: Rewrite with positive exponent

A negative exponent means reciprocal: $x^{-\frac{1}{2}} = \frac{1}{x^{\frac{1}{2}}}$

Answer:

$\frac{1}{x^{\frac{1}{2}}}$