Question
Find a single repeater machine that will do the same work as hook-up.
✓
Answer
Using law of exponents, $\left(a^m \times a^n=a^{m+n}\right)$$[\therefore$ a is non-zero integer$]$
Repeator machine can do the work is equal to $\big(\frac{1}{2}\big)^2\times\big(\frac{1}{3}\big)^2$
$=\frac{1}{2}\times\frac{1}{2}\times\frac{1}{3}\times\frac{1}{3}=\frac{1}{2\times3\times2\times3}=\frac{1}{(6)^2}$
so, $\Big(\text{x}\big(\frac{1}{6}\big)^2\Big)$ single machine can do the same work.
Repeator machine can do the work is equal to $\big(\frac{1}{2}\big)^2\times\big(\frac{1}{3}\big)^2$
$=\frac{1}{2}\times\frac{1}{2}\times\frac{1}{3}\times\frac{1}{3}=\frac{1}{2\times3\times2\times3}=\frac{1}{(6)^2}$
so, $\Big(\text{x}\big(\frac{1}{6}\big)^2\Big)$ single machine can do the same work.
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