Question

simplify.
\\(\frac{u^{\frac{5}{8}}}{u^{\frac{1}{2}}}\\)
write your answer using only a positive exponent.
assume that the variable represents a positive real number.

Explanation:

Step1: Use the quotient rule for exponents

When dividing two powers with the same base, we subtract the exponents: \( \frac{a^m}{a^n} = a^{m - n} \). Here, the base is \( u \), so we have \( u^{\frac{5}{8}} \div u^{\frac{1}{2}} = u^{\frac{5}{8}-\frac{1}{2}} \).

Step2: Subtract the exponents

First, find a common denominator for \( \frac{5}{8} \) and \( \frac{1}{2} \). The common denominator of 8 and 2 is 8. So, \( \frac{1}{2}=\frac{4}{8} \). Then, \( \frac{5}{8}-\frac{4}{8}=\frac{1}{8} \). So the expression simplifies to \( u^{\frac{1}{8}} \).

Answer:

\( u^{\frac{1}{8}} \)