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

  • question_answer
    Show that: \[\frac{{{x}^{a(b-c)}}}{{{x}^{b(a-c)}}}\div {{\left( \frac{{{x}^{b}}}{{{x}^{a}}} \right)}^{c}}=?\]

    A)  0                    

    B)  1          

    C)  2                    

    D)  \[{{2}^{(a+b+c)}}\]

    Correct Answer: B

    Solution :

    [b] We have, \[\frac{{{x}^{a(b-c)}}}{{{x}^{b(a-c)}}}\div {{\left( \frac{{{x}^{b}}}{{{x}^{a}}} \right)}^{c}}\] \[=\frac{{{x}^{ab-ac}}}{{{x}^{ba-bc}}}\div {{({{x}^{b-a}})}^{c}}\] \[={{x}^{(ab-ac)-(ba-bc)}}\times \frac{1}{{{x}^{(b-a)c}}}\] \[={{x}^{ab-ac-ba+bc}}\times \frac{1}{{{x}^{bc-ac}}}={{x}^{-ac+bc}}.{{x}^{ac-bc}}\] \[={{x}^{ac+bc+ac-bc)}}={{x}^{0}}=1\]


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