Question

use the quotient property to ...

question

simplify: \frac{\sqrt4{486m^{11}}}{\sqrt4{3m^4}}.

provide your answer below:

Explanation:

Apply the quotient property of radicals

$$ \frac{\sqrt[4]{486m^{11}}}{\sqrt[4]{3m^4}} = \sqrt[4]{\frac{486m^{11}}{3m^4}} $$

Simplify the radicand

$$ \frac{486}{3} = 162 $$

$$ \frac{m^{11}}{m^4} = m^{11-4} = m^7 $$

$$ \sqrt[4]{\frac{486m^{11}}{3m^4}} = \sqrt[4]{162m^7} $$

Simplify the fourth root

$$ 162 = 81 \times 2 = 3^4 \times 2 $$

$$ m^7 = m^4 \times m^3 $$

$$ \sqrt[4]{162m^7} = \sqrt[4]{3^4 \cdot m^4 \cdot 2m^3} = 3m\sqrt[4]{2m^3} $$

Answer:

Simplify: \(\frac{\sqrt[4]{486m^{11}}}{\sqrt[4]{3m^4}}\).

Provide your answer below:
<blank>\(3m\sqrt[4]{2m^3}\)</blank>