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# What is the remainder when 7 ^ 74 – 5 ^74 is divided by 4? (2008)

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#### What is the remainder when $({ 7 }^{ 74 }-{ 5 }^{ 74 })$ is divided by 4?

a.0       b.1          c.2        d. None of these [CAT, 2008]

### Solution:

#### The laws of exponents:

###### Now, divide  274    by 4. Firstly, we have to check whether the remainder of the division changes for odd or even integer:

Leave 1 as an exponent because then the numerator, 2, is not divisible by 4, the denominator.

#### Large even exponent:

###### See similar question no.1 See similar question no. 2See similar question no. 3

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