Question

simplify. assume all variables are positive. \\(\frac{x^{\frac{5}{2}}}{x^{\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 rule for division

When dividing two terms with the same base, we subtract the exponents: $ \frac{x^m}{x^n} = x^{m - n} $. Here, $ m = \frac{5}{2} $ and $ n = \frac{3}{2} $.
$$\frac{x^{\frac{5}{2}}}{x^{\frac{3}{2}}} = x^{\frac{5}{2} - \frac{3}{2}}$$

Step2: Subtract the exponents

Subtract the fractions in the exponent: $ \frac{5}{2} - \frac{3}{2} = \frac{5 - 3}{2} = \frac{2}{2} = 1 $.
So, $ x^{\frac{5}{2} - \frac{3}{2}} = x^1 = x $.

Answer:

$x$