How do you evaluate #\frac { 27^ { \frac { 2} { 3} } } { 27^ { \frac { 1} { 3} } }#?

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Answer 1 · 2017-03-04T22:40:56

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#1/(27^(1/3))# is the same as #27^(-1/3)#

So we can write: #27^(2/3)xx27^(-1/3)#

Another way of writing this is:

#27^(2/3-1/3)" "=" "27^(1/3)#

Which is the same as #root(3)(27)#

but #3xx3xx3=27#

so #27^(1/3)=root(3)(27)=3#