Question

8.5 divide radical expressions (homework) score: 10/14 answered: 11/14 question 12 simplify. assume all variables are nonnegative. $\frac{sqrt{64a^{28}b^{- 10}}}{sqrt{2a^{9}b^{-4}}}=$ question help: video written example

Explanation:

Step1: Use quotient - rule of radicals

$\frac{\sqrt{64a^{28}b^{- 10}}}{\sqrt{2a^{9}b^{-4}}}=\sqrt{\frac{64a^{28}b^{-10}}{2a^{9}b^{-4}}}$

Step2: Simplify the fraction inside the radical

$\sqrt{\frac{64}{2}\cdot\frac{a^{28}}{a^{9}}\cdot\frac{b^{-10}}{b^{-4}}}=\sqrt{32a^{28 - 9}b^{-10+4}}=\sqrt{32a^{19}b^{-6}}$

Step3: Rewrite and simplify the radical

$\sqrt{16\times2\times a^{18}\times a\times b^{-6}} = 4a^{9}b^{-3}\sqrt{2a}=\frac{4a^{9}\sqrt{2a}}{b^{3}}$

Answer:

$\frac{4a^{9}\sqrt{2a}}{b^{3}}$