How do you simplify #81^sqrt2 div 3^sqrt2#?

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Answer 1 · 2016-11-15T05:42:08

#3^(3sqrt2)=27^sqrt2#

We can take our original:

#81^sqrt2-:3^sqrt2#

and rewrite it this way:

#(3^4)^sqrt2/3^sqrt2#

which can then be written as:

#(3^(4sqrt2))/(3^sqrt2)#

and then we can write it as:

#(3^(3sqrt2+sqrt2))/(3^sqrt2)=(3^(3sqrt2)xx3^sqrt2)/(3^sqrt2)#

cancel the two like terms and get:

#(3^(3sqrt2)xxcancel(3^sqrt2))/cancel(3^sqrt2)=3^(3sqrt2)=27^sqrt2#