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

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Answer 1 · 2017-06-02T08:37:13

#15m^2#

Step 1. Use rule of division of same roots.

#(5 root(3)(108m^7))/(root(3)(4m))=5 root(3)((108m^7)/(4m))#

Step 2. Divide numbers inside cube root.

#=5 root(3)((108m^7)/(4m))=5 root(3)(27m^6)#

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

#=5 root(3)(27m^6)=5 root(3)(3^3(m^2)^3)#

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

#=5 root(3)(3^3(m^2)^3)=5(3)m^2=15m^2#