Question

simplify. assume all variables are positive.
\\(\frac{w^{\frac{5}{2}}}{w^{\frac{3}{2}}}\\)
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: Use exponent - division rule

When dividing two powers with the same base \(a^m\div a^n=a^{m - n}\). Here the base is \(w\), \(m=\frac{5}{2}\) and \(n=\frac{3}{2}\). So \(w^{\frac{5}{2}}\div w^{\frac{3}{2}}=w^{\frac{5}{2}-\frac{3}{2}}\).

Step2: Calculate the exponent

\(\frac{5}{2}-\frac{3}{2}=\frac{5 - 3}{2}=\frac{2}{2}=1\). So \(w^{\frac{5}{2}-\frac{3}{2}}=w^1 = w\).

Answer:

\(w\)