Question

8.3 simplify rational exponents (homework)
score: 16.05/25 answered: 17/25
question 18
simplify by writing as a single exponential expression. assume all variables are positive.
\\(\frac{a^{\frac{3}{2}}}{a^{\frac{1}{2}}}=\\)
question help: video written example

Explanation:

Step1: Apply exponent - division rule

When dividing two exponential expressions with the same base $a$ ($a>0$), $\frac{a^m}{a^n}=a^{m - n}$. Here, $m=\frac{3}{2}$ and $n = \frac{1}{2}$.
$a^{\frac{3}{2}}\div a^{\frac{1}{2}}=a^{\frac{3}{2}-\frac{1}{2}}$

Step2: Calculate the exponent

Subtract the fractions: $\frac{3}{2}-\frac{1}{2}=\frac{3 - 1}{2}=\frac{2}{2}=1$.
$a^{\frac{3}{2}-\frac{1}{2}}=a^1=a$

Answer:

$a$