Question

A. Simplify: a) 6^0 + 9^0 b) 1^0 - 3^0 + (1/5) ^0 c) 7^0 × 8^0 ÷ 9^0 B. Write true or false: a) ( -1) ^odd positive integer = - 1 b) ( -1) ^ even positive integer = 1 c) (1) ^ even positive integer = - 1​

Answer 1

Step-by-step explanation:

Any positive integer is of the form 4q+1or4q+3

As per Euclid’s Division lemma.

If a and b are two positive integers, then,

a=bq+r

Where 0≤r<b.

Let positive integers be a.and b=4

Hence,a=bq+r

Where, (0≤r<4)

R is an integer greater than or equal to 0 and less than 4

Hence, r can be either 0,1,2and3

Now, If r=1

Then, our be equation is becomes

a=bq+r

a=4q+1

This will always be odd integer.

Now, If r=3

Then, our be equation is becomes

a=bq+r

a=4q+3

This will always be odd integer.

Hence proved.

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