Question

Question 149

Repeater Machine
Similarly, repeater machine is a hypothetical machine which automatically enlarges items several times. e.g. Sending a piece of wire through a $(\times 2^4)$ machine is the same as putting it through a $(\times 2)$ machine four times.
So, if you send a 3 cm piece of wire thorugh a $(\times 2{)}^4$ machine, its length becomes $3\times 2\times 2\times 2\times 2=48cm.$ It can also be written that a base (2) machine is being applied 4 times.

What will be the new length of a 4 cm strip inserted in the machine?

Answer 1

According to the question, if we put a 3 cm piece of wire through a $(\times 2^4)$ machine, its length becomes $3\times 2\times 2\times 2\times 2=48$ cm.
Similarly, 4 cm long strip becomes $4\times 2\times 2\times 2\times 2=64$ cm.