MathematicsSimplify using laws of exponent 



Simplify using laws of exponent
 


  1. A
    9
  2. B
    -3
  3. C
    4
  4. D
    -8
     

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    Solution:

    We know from exponentiation that when any real number b is multiplied with itself say n times we can write as
    We read as “b to the power n”. Here b is called base and n is called exponents, index, order or power. 
    In symbols for some real numbers 

    In symbols,

    We know from the law of zero power that any number raised to the power zero is equal to 1.

    The given numerical expression is

    We follow the BODMAS rule and open the bracket using distributive law of addition and multiplication to have
     We use the law of product with same base for in the first term and for  in the second term in the above step.we have

    use the law of zero power for the first term of the above step and have . We proceed,
     
    We find the prime factorization of 64 and replace 64 as
    in the above step. We have
     We use the law of power of power   for  in the above step and have,
    So the correct option is 2.
     
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