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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:$$\left(\frac15\right)^{y - x}$$

 Jan 15, 2020
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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

 

 

cool cool cool

 Jan 16, 2020

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