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Railways Quantitative Aptitude Power, Surds And Indices Sample Paper Surds Indices Sample Test Paper-4

  • question_answer
    Simplify: \[{{\left( \frac{{{2}^{a}}}{{{2}^{b}}} \right)}^{a+b}}{{\left( \frac{{{2}^{b}}}{{{2}^{c}}} \right)}^{b+c}}{{\left( \frac{{{2}^{c}}}{{{2}^{a}}} \right)}^{c+a}}\]

    A)   0                   

    B)  1          

    C)   2       

    D)  \[{{(2)}^{a+b+c}}\]

    Correct Answer: B

    Solution :

    [b] \[{{\left( \frac{{{2}^{a}}}{{{2}^{b}}} \right)}^{a+b}}{{\left( \frac{{{2}^{b}}}{{{2}^{c}}} \right)}^{b+c}}{{\left( \frac{{{2}^{c}}}{{{2}^{a}}} \right)}^{c+a}}\] \[={{({{2}^{a-b}})}^{a+b}}.{{({{2}^{b-c}})}^{b+c}}.{{({{2}^{c-a}})}^{c+a}}\]             \[=2({{a}^{2}}-{{b}^{2}})+({{b}^{2}}-{{c}^{2}})+({{c}^{2}}-{{a}^{2}})={{2}^{0}}=1\]


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