8. A proof by contradiction uses the fact that you are proving a statement which

Question

8. A proof by contradiction uses the fact that you are proving a statement which, by definition, must be true or false. By assuming it is false and arriving at a contradiction, we can safely assume that our assumption must be incorrect and therefore the original statement must be true.

9. In a proof by contraposition, we take advantage of the fact that a conditional statement is logically equivalent to its converse. Thus we assume that the conclusion is true and show that the hypothesis must be true.

Explanation / Answer

6)

we can claculate this by factorization method

divide the given numbers into factors

(45^8) = (3 * 3 * 5) ^ 8 (88^5) = (2 * 2 * 2 * 11) ^ 5

If you put it back together as separate factors you get something like this

(3^16) * (5^8) * (2^15) * (11^5)

now you can find the number of zeroes by figuring out how many factors of 10 (which equals 2 * 5) you can make.

You can make 8 factors of 10 so it looks like (3 ^ 16) * (2 ^ 7) * (11 ^ 5) * ((2*5) ^ 8)

= (3 ^ 16) * (2 ^ 7) * (11 ^ 5) * (10 ^ 8)
hence there will be 8 zeros

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