Let $2^x$ be the greatest power of $2$ that is a factor of $144$, and let $3^y$ be the greatest power of $3$ that is a factor of $144$. Evaluate the following expression:$$\left(\frac15\right)^{y - x}$$
144 =
12 * 12 =
2^2 * 3 * 2^2 * 3
2^4 * 3^2
The greatest power of 2 that is a factor of 144 is 2^4 ⇒ x = 4
The greatest power of 3 that is a factor of 144 is 3^2 ⇒ y = 2
So
(1/5)y - x = (1/5)2 - 4 = (1/5)-2 = 52 = 25
+35 
