Question

simplify. assume all variables are positive.
\\(\frac{d^{\frac{3}{2}}}{d^{\frac{5}{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 terms with the same base $a^m\div a^n=a^{m - n}$, here the base is $d$, $m=\frac{3}{2}$ and $n=\frac{5}{2}$. So $\frac{d^{\frac{3}{2}}}{d^{\frac{5}{2}}}=d^{\frac{3}{2}-\frac{5}{2}}$.

Step2: Calculate the exponent

$\frac{3}{2}-\frac{5}{2}=\frac{3 - 5}{2}=\frac{-2}{2}=-1$. So we have $d^{-1}$.

Step3: Make the exponent positive

Using the rule $a^{-n}=\frac{1}{a^{n}}$, for $a = d$ and $n = 1$, $d^{-1}=\frac{1}{d}$.

Answer:

$\frac{1}{d}$