Question 254892
Take note that the LCD of the denominators in the exponents is 6. So you can rewrite each fraction with a denominator of 6. So for {{{1/2}}}, multiply it by {{{3/3}}} to get {{{3/6}}}. Likewise, multiply {{{2/3}}} by {{{2/2}}} to get {{{4/6}}}.



So the expression {{{x^(1/2)y^(2/3)z^(5/6)^""}}} then can be rewritten as {{{x^(3/6)y^(4/6)z^(5/6)^""}}}



Now use the identity {{{x^(yz)=(x^y)^z}}} to convert {{{x^(3/6)y^(4/6)z^(5/6)^""}}} into {{{(x^3y^4z^5)^(1/6)}}}.



Finally, convert to radical notation to get {{{root(6,x^3y^4z^5)}}}



So {{{x^(1/2)y^(2/3)z^(5/6)^""=root(6,x^3y^4z^5)}}} where every variable is non-negative.