Question

use the properties of rational exponents to simplify $\frac{6}{6^{1/4}}$.○ $6^{-3/4}$○ $6^{1/4}$○ $6^{3/4}$○ $6^{5/4}$

Explanation:

Step1: Rewrite numerator with exponent

$6 = 6^1$

Step2: Apply exponent subtraction rule

$\frac{6^1}{6^{1/4}} = 6^{1 - \frac{1}{4}}$

Step3: Calculate the exponent

$1 - \frac{1}{4} = \frac{4}{4} - \frac{1}{4} = \frac{3}{4}$

Answer:

$\boldsymbol{6^{3/4}}$ (the third option: $6^{3/4}$)