Question

Question 159(vi)

Find a single repeater machine that will do the same work as each hook-up.

Answer 1

Using law of exponents, $a^m\times a^n=a^{m+n}$ [$\because$ a is non-zero integer]
Repeator machine can do the work is equal to ${\left(\frac{1}{2}\right)}^2\times {\left(\frac{1}{3}\right)}^2=\frac{1}{2}\times \frac{1}{2}\times \frac{1}{3}\times \frac{1}{3}=\times \frac{1}{2\times 3\times 2\times 3}=\times \frac{1}{(6{)}^2}So,(\times {\left(\frac{1}{6}\right)}^2)$ single machine can do the same work.g47