How do you simplify #\root[ 3] { 448h ^ { 4} b ^ { 2} }#?

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Answer 1 · 2017-09-24T05:16:42

# 4 * (7h ^4 b^2 )^ (1/3) #
or
# 4* \root[ 3] { 7h ^ { 4} b ^ { 2} }#

#\root[ 3] { 448h ^ { 4} b ^ { 2} }#

Third root (or cube root) can be written as

=# [ 448h ^ 4 b ^ 2] ^ (1/3)#

= # [ (64 * 7 ) h ^ 4 b ^ 2] ^ (1/3)#

=# [ ((4^3) * 7 ) h ^ 4 b ^ 2] ^ (1/3)# ----- # (a^m)^n = a^(mn)#

=# [ (4^3)^ (1/3) * (7 )^ (1/3) h ^ (4/3) b ^ (2/3)] #

= # [4 * (7 )^ (1/3) h ^ (4/3) b ^ (2/3)] #

= # [4 * (7h ^4 b^2 )^ (1/3) ] # or

= # 4* \root[ 3] { 7h ^ { 4} b ^ { 2} }#