Question

simplify.
\\(\frac{u^{\frac{1}{2}}}{u^{\frac{6}{7}}}\\)
write your answer using only a positive exponent.
assume that the variable represents a positive real number.

Explanation:

Step1: Apply exponent division rule

When dividing like bases, subtract exponents: $\frac{u^a}{u^b}=u^{a-b}$.
So $\frac{u^{\frac{1}{2}}}{u^{\frac{6}{7}}}=u^{\frac{1}{2}-\frac{6}{7}}$

Step2: Compute exponent difference

Find common denominator (14) to subtract fractions:
$\frac{1}{2}-\frac{6}{7}=\frac{7}{14}-\frac{12}{14}=-\frac{5}{14}$

Step3: Convert to positive exponent

Use $u^{-n}=\frac{1}{u^n}$ to rewrite:
$u^{-\frac{5}{14}}=\frac{1}{u^{\frac{5}{14}}}$

Answer:

$\frac{1}{u^{\frac{5}{14}}}$