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(a) compute \(10^{999}\cdot 5^{-999}\cdot 2^{-999}\).

 

(b) Suppose we write down the smallest positive 2-digit, 3-digit, and 4-digit multiples of 9.

What is the sum of these three numbers?

 

(c) Suppose we write down the smallest (positive) 2-digit, 3-digit, and 4-digit multiples of 8.

What is the sum of these three numbers?

 

(d)Suppose we write down the smallest (positive) 2-digit, 3-digit, and 4-digit multiples of 7.

What is the sum of these three numbers?

 

(e)What is the sum of all positive 1-digit integers that 4221462 is divisible by?

 

(f)What's the largest -digit number that is a multiple of both 4 and 9?

 Jan 16, 2021
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a) 10^999=5^999*2^999

5^999*5^-999*2^999*2^-999=1*1=1

 

b)

Smallest 2 digits- 18

Smallest 3 digits- 108

Smallest 4 digits- 1008

18+108+1008=1134

 

c)

2 digits- 16

3 digits- 104

4 digits- 1000

16+104+1000=1120

 

d) 

2 digit- 14

3 digit- 105

4 digit- 1001

14+105+1001=1120

 

e)

1, 2, 3, 6, 7

Add them

 Jan 16, 2021

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