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If \(12^2 \cdot 18^3 = 2^x \cdot 3^y\), find x+y.

 Aug 2, 2020
 #1
avatar+1035 
+4

Since both 2 and 3 are prime numbers, we should find the prime factorization of \(12^2\cdot18^3\). So:

12 = 2*2*3

12=2*2*3

18=2*3*3

18=2*3*3

18=2*3*3

As you see, we have 8 3's and 7 2'. So, 8+7 is \(\boxed{15}\)

 

:)

 Aug 2, 2020
 #2
avatar+27644 
+1

 

  122        *      183

(2*2*3)2   *  (2*3*3)3

22+2+3     *   32+3+3

27            *    38             now you can  see x and y    (as ilorty found)

 Aug 2, 2020

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