Question

current objective
use the quotient property to simplify a perfect square fraction

question

simplify: \\(\sqrt{\frac{y^7}{y^{21}}}\\). (you may assume any variables are greater than zero.)

provide your answer below:

Explanation:

Simplify the fraction inside the radical

$$ \frac{y^7}{y^{21}} = y^{7 - 21} = y^{-14} = \frac{1}{y^{14}} $$

Apply the square root to the simplified expression

$$ \sqrt{\frac{1}{y^{14}}} = \frac{\sqrt{1}}{\sqrt{y^{14}}} = \frac{1}{y^7} $$

Answer:

Simplify: <blank>\(\frac{1}{y^7}\)</blank>