How do you simplify #(2x^6^m)/(6x^2^m)#?

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Answer 1 · 2015-07-01T22:06:38

#((x^4)/3)^m if x in RR-{0}, m in RR#

Step 1 : The domain of the function.

We have only one forbidden value, when #x=0#. This is the only value where your denominator equal 0. And we can't divide by 0...

Therefore, the domain of our function is : #RR - {0}# for #x# and #RR# for #m#.

Step 2 : Factoring power m

#(2x^6 ^m)/(6x^2 ^m)# <=> #(2x^6)^m/(6x^2)^m# <=> #((2x^6)/(6x^2))^m#

Step 3 : Simplify the fraction

#((2x^6)/(6x^2))^m# <=> #((x^6)/(3x^2))^m# <=> #((x^4)/(3))^m#

Don't forget, #x !=0#