If \(x^{a+3}=y^{b+2},\) where \(x\) and \(y\) are distinct prime numbers, what is the value of \(ab?\)
A. -6
B. 0
C. 5
D. 6
E. It cannot be determined from the information provided.
Answer: D
Source: Princeton Review
If \(x^{a+3}=y^{b+2},\) where \(x\) and \(y\) are distinct prime numbers, what is the value of \(ab?\)
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A prime number raised to a power has only that prime number and powers of that number as factors, except when that power is 0, in which case any prime number raised to that power equals 1.
So X^(a+3)=1=Y^(b+2)
a+3= 0=b+2
a=-3 and b=-2
ab=6,D
So X^(a+3)=1=Y^(b+2)
a+3= 0=b+2
a=-3 and b=-2
ab=6,D