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