2E What is the greatest whole number less than 1000 that: (1) can be expressed as the sum of two consecutive whole numbers, and
(2) can be expressed as the sum of three consecutive whole numbers, and
(3) can be expressed as the sum of five consecutive whole numbers

(1) 499 and 500 are the greatest consecutive whole numbers whose sum is less than 1000.

(2) 332, 333 and 334 are the greatest consecutive whole numbers whose sum is less than 1000.

(3) 197, 198, 199, 200 and 201 are the greatest consecutive whole numbers whose sum is less than 1000.

Step-by-step explanation:

(1) Let be , such that:

(Eq. 1)

Then we solve the inequation by algebraic means:

Which means that greatest value of is 499. In consequence, 499 and 500 are the greatest consecutive whole numbers whose sum is less than 1000.

(2) Let be , such that:

(Eq. 2)

Then we solve the inequation by algebraic means:

Which means that greatest value of is 332. In consequence, 332, 333 and 334 are the greatest consecutive whole numbers whose sum is less than 1000.

(3) Let be , such that:

(Eq. 3)

Then we solve the inequation by algebraic means:

Which means that greatest value of is 197. In consequence, 197, 198, 199, 200 and 201 are the greatest consecutive whole numbers whose sum is less than 1000.

use the power rule  

( a b ) n = a n b n

to distribute the exponent.

apply the product rule to  

3 x 2 y 3 . ( 3 x 2 ) 2 ( y 3 ) 2

apply the product rule to  

3 x 2 . 3 2 ( x 2 ) 2 ( y 3 ) 2

raise  

3

to the power of  

2 . 9 ( x 2 ) 2 ( y 3 ) 2 multiply the exponents in   ( x 2 ) 2

.

apply the power rule and multiply exponents,  

( a m ) n = a m n . 9 x 2 ⋅ 2 ( y 3 ) 2

multiply  

2   by   2 . 9 x 4 ( y 3 ) 2

multiply the exponents in  

( y 3 ) 2 .

apply the power rule and multiply exponents,  

( a m ) n = a m n . 9 x 4 y 3

⋅

2

multiply  

3   by   2 . 9 x 4 y 6

step-by-step explanation: