If (2^x)(3^y)=288, where x and y are positive integers, then (2^x−1)(3^y−2) equals:

A. 16B. 24C. 48D. 96E. 144

Question

If (2^x)(3^y)=288, where x and y are positive integers, then (2^x−1)(3^y−2) equals:

A. 16B. 24C. 48D. 96E. 144

Raju · Answer

prime factorization of 288 = 2^5*3^2. With that it is easy to count the 5 twos and the 2 threes that are the prime factors. So x=5, y=2. now quickly 2^4(3^0)= 16*1 = 16 Answer . A

	Raju
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Top Contributors

mahesh

4 months, 2 weeks ago

If (2^x)(3^y)=288, where x and y are positive integers, then (2^x−1)(3^y−2) equals:
A. 16
B. 24
C. 48
D. 96
E. 144

Top Contributors

mahesh

4 months, 2 weeks ago

If (2^x)(3^y)=288, where x and y are positive integers, then (2^x−1)(3^y−2) equals:A. 16B. 24C. 48D. 96E. 144

If (2^x)(3^y)=288, where x and y are positive integers, then (2^x−1)(3^y−2) equals:
A. 16
B. 24
C. 48
D. 96
E. 144