Question

simplify. assume all variables are positive. \\(\frac{w^{\frac{3}{2}}}{w^{\frac{1}{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 rule for division

When dividing exponents with the same base, subtract the exponents: $a^m \div a^n = a^{m - n}$. Here, the base is $w$, $m = \frac{3}{2}$, and $n = \frac{1}{2}$. So we have $w^{\frac{3}{2} - \frac{1}{2}}$.

Step2: Subtract the exponents

Calculate $\frac{3}{2} - \frac{1}{2} = \frac{2}{2} = 1$. So the expression simplifies to $w^1$.

Step3: Simplify $w^1$

Any number or variable to the power of 1 is itself, so $w^1 = w$.

Answer:

$w$