Question

question
use the properties of exponents to determine the value of ( a ) for the equation below given ( x > 0 ).
( \frac{sqrt6{x}}{left(x^{5}
ight)^{\frac{1}{6}}} = x^{a} )

Explanation:

Step1: Rewrite roots as exponents

$\frac{x^{\frac{1}{6}}}{(x^5)^{\frac{1}{6}}}$

Step2: Simplify denominator exponent

$\frac{x^{\frac{1}{6}}}{x^{\frac{5}{6}}}$

Step3: Subtract exponents (division rule)

$x^{\frac{1}{6}-\frac{5}{6}}$

Step4: Calculate the exponent value

$x^{\frac{1-5}{6}} = x^{-\frac{4}{6}} = x^{-\frac{2}{3}}$

Answer:

$-\frac{2}{3}$