Question

pls answer this question
pls don't answer spam or wrong if you send you are a son of b#$@h​

Answer 1

Answer:

$= {x}^{a \times \frac{1}{ab} } \div {x}^{b \times \frac{1}{ab} } \times {x}^{b \times \frac{1}{bc} } \div {x}^{c \times \frac{1}{bc} } \times {x}^{c \times \frac{1}{ca} } \div {x}^{a \times \frac{1}{ca} } \\ = {x}^{ \frac{1}{b } - \frac{1}{a} + \frac{1}{c} - \frac{1}{b} + \frac{1}{a} - \frac{1}{c} } \\ = {x}^{0 } \\ = 1$

Answer 2

Solution :-

$\longmapsto \sf\left(\dfrac{x^a}{x^b}\right)^{\frac{1}{ab}}\times\left(\dfrac{x^b}{x^c}\right)^{\frac{1}{bc}}\times\left(\dfrac{x^c}{x^a}\right)^{\frac{1}{ac}}$

Simplifying using ,

• $\sf\left(\dfrac{a}{b}\right)^m = \dfrac{a^m}{b^m}$

$\longmapsto\sf\dfrac{x^{1/b}}{x^{1/a}}\times\dfrac{x^{1/c}}{x^{1/b}}\times\dfrac{x^{1/a}}{x^{1/c}}$

$\sf\longmapsto \dfrac{\cancel{x^{1/b}}}{\cancel{x^{1/a}}}\times\dfrac{\cancel{x^{1/c}}}{\cancel{x^{1/b}}}\times\dfrac{\cancel{x^{1/a}}}{\cancel{x^{1/c}}}$

$\longmapsto \sf\left(\dfrac{x^a}{x^b}\right)^{\frac{1}{ab}}\times\left(\dfrac{x^b}{x^c}\right)^{\frac{1}{bc}}\times\left(\dfrac{x^c}{x^a}\right)^{\frac{1}{ac}}=\underline{\boxed{\textbf{\textsf{1}}}}$

$\therefore\orange{\sf Hence ,\left(\dfrac{x^a}{x^b}\right)^{\frac{1}{ab}}\times\left(\dfrac{x^b}{x^c}\right)^{\frac{1}{bc}}\times\left(\dfrac{x^c}{x^a}\right)^{\frac{1}{ac}}}=\underline{\boxed{\textbf{\textsf{1}}}}$