Question

plz solve this fast plzzzzzzzz

Answer 1

[tex] ( \frac{ x^{a} }{ x^{b} } )^{a+b} + ( \frac{ x^{b} }{ x^{c} } )^{b+c} + ( \frac{ x^{c} }{ x^{a} } )^{c+a} \\ = \frac{ x^{ a^{2}+ab } }{ x^{ab+ b^{2} } } +\frac{ x^{ b^{2}+bc } }{ x^{bc+c^{2} } } +\frac{ x^{ c^{2}+ac } }{ x^{ac+ a^{2} } } \\ = x^{ a^{2} +ab-ab- b^{2} }+ x^{ b^{2} +bc-bc- c^{2} }+x^{ c^{2} +ac-ac- a^{2} } \\ = x^{ a^{2}- b^{2} } +x^{ b^{2}- c^{2} } +x^{ c^{2}- a^{2} } [/tex]

Answer 2

ANSWER OF FIRST QUESTION
$( \frac{x^{a}}{x^{b}})^{a+b} * ( \frac{x^{b}}{x^{c}})^{b+c} * ( \frac{x^{c}}{x^{a}})^{c+a}$
$= (x^{a-b})^{a+b} * (x^{b-c})^{b+c} * (x^{c-a})^{c+a}$
$= x^{(a-b)(a+b)} * x^{(b-c)(b+c)} * x^{(c-a)(c+a)}$
$= x^{(a-b)(a+b)+(b-c)(b+c)+(c-a)(c+a)}$
$= x^{a^{2}-b^{2}+b^{2}-c^{2}+c^{2}-a^{2}}$
$= x^{a^{2}-a^{2}-b^{2}+b^{2}-c^{2}+c^{2}}$
$= x^{0}$
$= 1$

ANSWER OF SECOND QUESTION
$[5(8^{ \frac{1}{3}}+27^{ \frac{1}{3}})^{3}]^{ \frac{1}{4}}$
$= [5( \sqrt[3]{8}+ \sqrt[3]{27})^{3}]^{ \frac{1}{4}}$
$= [5(2+3)^{3}]^{ \frac{1}{4}}$
$= [5(5)^{3}]^{ \frac{1}{4}}$
$= [5^{1}*5^{3}]^{ \frac{1}{4}}$
$= [5^{1+3}]^{ \frac{1}{4}}$
$= [5^{4}]^{ \frac{1}{4}}$
$= 5^{4* \frac{1}{4}}$
$= 5^{1}$
$= 5$

Hope THESE may help you.