Question

use rational exponents to simplify the following radical expression (sqrt10{16x^{8}y^{6}}) (sqrt10{16x^{8}y^{6}}=square) (simplify your answer. type an exact answer, using radicals as needed.)

Explanation:

Step1: Convert radical to rational exponents

$\sqrt[10]{16x^8y^6} = (16x^8y^6)^{\frac{1}{10}}$

Step2: Distribute exponent to each term

$= 16^{\frac{1}{10}} \cdot x^{\frac{8}{10}} \cdot y^{\frac{6}{10}}$

Step3: Simplify exponents and rewrite

$= (2^4)^{\frac{1}{10}} \cdot x^{\frac{4}{5}} \cdot y^{\frac{3}{5}}$
$= 2^{\frac{4}{10}} \cdot x^{\frac{4}{5}} \cdot y^{\frac{3}{5}}$
$= 2^{\frac{2}{5}} \cdot x^{\frac{4}{5}} \cdot y^{\frac{3}{5}}$

Step4: Convert back to radical form

$= \sqrt[5]{2^2x^4y^3}$
$= \sqrt[5]{4x^4y^3}$

Answer:

$\sqrt[5]{4x^4y^3}$