Questions: Simplify the expression x^-1/2 x^5/2 / x^1/3

Solution Steps

To simplify the given expression, we can use the properties of exponents. Specifically, we can combine the exponents in the numerator and then subtract the exponent in the denominator.

First, we combine the exponents in the numerator: \[ x^{-\frac{1}{2}} \cdot x^{\frac{5}{2}} = x^{-\frac{1}{2} + \frac{5}{2}} = x^{\frac{4}{2}} = x^2 \]

Next, we subtract the exponent in the denominator from the combined exponent in the numerator: \[ \frac{x^2}{x^{\frac{1}{3}}} = x^{2 - \frac{1}{3}} = x^{\frac{6}{3} - \frac{1}{3}} = x^{\frac{5}{3}} \]

Final Answer