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8th Class Mathematics Exponents and Power Question Bank Exponents and Powers

  • question_answer
    What is the simplified form of \[\frac{{{\left( {{x}^{a+b}} \right)}^{3}}.{{\left( {{x}^{b+c}} \right)}^{3}}.{{\left( {{x}^{c+a}} \right)}^{3}}}{{{\left( {{x}^{a}}.{{x}^{b}}.{{x}^{c}} \right)}^{6}}}\]?

    A)          \[0\]                                    

    B)  \[1\]                    

    C)                  \[{{x}^{a+b+c}}\]           

    D)         \[x\]                                                   

    Correct Answer: B

    Solution :

    The given expression \[=\frac{{{x}^{3a+3b}}.{{x}^{3b+3c}}.{{x}^{3c+3a}}}{{{x}^{6a+6b+6c}}}\] \[=\frac{{{x}^{3a+3b+3b+3c+3c+3a}}}{{{x}^{6a+6b+6c}}}=\frac{{{x}^{6a+6b+6c}}}{{{x}^{6a+6b+6c}}}\] \[={{x}^{6a+6b+6c-6a-6b-6c}}={{x}^{0}}=1\]


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