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Q.

Express 64 729 − 1 6   in the simplest form.


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a

2 3  

b

3 2  

c

4 3  

d

3 4   

answer is B.

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Detailed Solution

We have the expression as follows,
64 729 − 1 6  
To simplify the expression, first convert the negative exponent to positive.
64 729 − 1 6 = 729 64 1 6  
First do prime factorization of both the numerator and the denominator then use the power of quotient property and the property of a power raised to another power.
729 64 1 6 = 3×3×3×3×3×3 2×2×2×2×2×2 1 6 = 3 6 2 6 1 6 = 3 2 6× 1 6 = 3 2  
So, the simplest form of 64 729 − 1 6   is obtained as  3 2  .
Hence, the correct option is (2).
 
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