Question

Prove that $[y^{a}/y^b]^1^/^a^b$ × $[y^{b}/y^c]^1^/^b^c$ × $[y^{c}/y^a]^1^/^c^a$ = 1

SUPER URGENT!!!!! PLEASE!!!!!

Answer 1

$y^{a-b})^{\frac{1}{ab}} * (y^{b-c})^{\frac{1}{bc}} * (y^{c-a})^{\frac{1}{ca}} \\ \\ \\ (y^{\frac{a-b}{ab}}) * (y^{\frac{b-c}{bc}}) * (y^{\frac{c-a}{ca}}}) \\ \\ y^{\frac{a-b}{ab}+{\frac{b-c}{bc}}+{\frac{c-a}{ca}}} \\ \\ y^{\frac{ca-cb+ab-ac+bc-ba}{abc}} \\ \\ y^{0/abc} = 1$

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another way

$(\frac {y^{a}}{y^b})^{\frac{1}{ab}} * (\frac {y^{b}}{y^c})^{\frac{1}{bc}} * (\frac {y^{c}}{y^a})^{\frac{1}{ca}} \\ \\ (\frac {y^{a/ab}}{y^{b/ab}}) * (\frac {y^{b/bc}}{y^{c/bc}}) * (\frac {y^{c/ca}}{y^{a/ca}}) \\ \\ (\frac {y^{1/b}}{y^{1/a}}) * (\frac {y^{1/c}}{y^{1/b}}) * (\frac {y^{1/a}}{y^{1/c}}) \\ \\ \frac {y^{1/b}}{y^{1/a}} * \frac {y^{1/c}}{y^{1/b}} * \frac {y^{1/a}}{y^{1/c}} \\ \\ = 1$

As the terms cancel in the numerator and denominator, you get 1.