How do you simplify $\frac{5 \sqrt[3]{108 m^{7}}}{\sqrt[3]{4 m}}$ $\frac { 5\root[ 3] { 108m ^ { 7} } } { \root [ 3] { 4m } }$ ?

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Answer 1 · 2017-06-02T08:37:13

$15 m^{2}$ $15m^2$

Step 1. Use rule of division of same roots.

$\frac{5 \sqrt[3]{108 m^{7}}}{\sqrt[3]{4 m}} = 5 \sqrt[3]{\frac{108 m^{7}}{4 m}}$ $(5 root(3)(108m^7))/(root(3)(4m))=5 root(3)((108m^7)/(4m))$

Step 2. Divide numbers inside cube root.

$= 5 \sqrt[3]{\frac{108 m^{7}}{4 m}} = 5 \sqrt[3]{27 m^{6}}$ $=5 root(3)((108m^7)/(4m))=5 root(3)(27m^6)$

Step 3. Express terms inside cube root as perfect cubes.

$= 5 \sqrt[3]{27 m^{6}} = 5 \sqrt[3]{3^{3} {(m^{2})}^{3}}$ $=5 root(3)(27m^6)=5 root(3)(3^3(m^2)^3)$

Step 4. Pull perfect cubes out of the cube root.

$= 5 \sqrt[3]{3^{3} {(m^{2})}^{3}} = 5 (3) m^{2} = 15 m^{2}$ $=5 root(3)(3^3(m^2)^3)=5(3)m^2=15m^2$

How do you simplify 53√108m73√4m\frac { 5\root[ 3] { 108m ^ { 7} } } { \root [ 3] { 4m } }?