64 raised to power 2/3 ?

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Answer 1 · 2018-06-28T05:55:57

#16#

Exponential law:

#a^(1/2)# = #sqrta#

#a^(1/3)# = #root(3)a#

So, #64^(2/3)# = #root(3)(64^2)# = #root(3)(8 xx 8 xx 8 xx 8)#

#root(3)(8 xx 8 xx 8 xx 8)# = #root(3)(8 xx 8 xx 8 xx 2 xx 2 xx 2)#

We know that,

#root(3)(8 xx 8 xx 8)# = #8#

#root(3)( 2 xx 2 xx 2)# = #2#

Therefore:

#64^(2/3)# = #root(3)(8 xx 8 xx 8 xx 2 xx 2 xx 2)# = #8 xx 2# = #16#

Answer 2 · 2018-06-28T06:25:25

#color(red)(=> 16#

#(64)^(2/3)#

#=> ((64) ^2)^(1/3)#

#=> (8 * 8 * 8 * 8)^(1/3)#

#=> (8 * 8 * 8)^(1/3) * 8^(1/3)#

#=> 8 * (2 * 2 * 2)^(1/3)#

#color(red)(=> 8 * 2 = 16#