Acertain plastic cup is manufactured by a robot. if 5 such robots, working at the same individual rate, can manufacture a combined total of 5 cups in 5 seconds, how many seconds will it take 25 robots to manufacture a total of 25 cups? a) 25b) 20c) 15d) 10e) 5

E) 5 seconds

Step-by-step explanation:

We know that 5 robots can manufacture 5 cups in 5 seconds.

   R1,R2,R3,R4,R5: 5 cups in 5 seconds

If we have 25 robots we can divide these 25 robots in 5 groups having 5 robots in each group. And each group will manufacture 5 cups in 5 seconds.

Team 1 - R1,R2,R3,R4,R5 : 5 cups in 5 seconds

Team 2 - R6,R7,R8,R9,R10: 5 cups in 5 seconds

Team 3 - R11,R12,R13,R14,R15: 5 cups in 5 seconds

Team 4 - R16,R17,R18,R19,R20: 5 cups in 5 seconds

Team 5 - R21,R22,R23,R24,R25: 5 cups in 5 secods

Then we have:

Meaning that if we have the 25 robots working simultaneously, it will take 5 seconds to each of the 5 teams (being a total of 25 robtos) to manufacture a total of 25 cups.

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: