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Q.

Use the laws of exponents to simplify 125 − 1 3   and choose the correct option.


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a

5

b

-5

c

1 5  

d

− 1 5   

answer is D.

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Detailed Solution

We have to simplify the expression given as follows,
125 − 1 3  .
We can rewrite the given expression with using the law a −b = 1 a b   and express 125 as a product of prime factors.
125 − 1 3 = 1 125 1 3 = 1 125 1 3 = 1 5×5×5 1 3 = 1 5 3 1 3  
Now, we further simplify the expression using the law x a 1 b = x a b  , as follows,
1 5 3 1 3 = 1 5 3× 1 3 = 1 5 1 = 1 5  
So, 125 − 1 3   is simplified as 1 5  .
Hence, the correct option is (4).
 
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Use the laws of exponents to simplify 125 − 1 3   and choose the correct option.