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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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If \(x^{a+3}=y^{b+2},\) where \(x\) and \(y\) are distinct prime numbers, what is the value of \(ab?\)

by Vincen » Fri Feb 11, 2022 3:18 am

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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
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Re: If \(x^{a+3}=y^{b+2},\) where \(x\) and \(y\) are distinct prime numbers, what is the value of \(ab?\)

by regor60 » Sun Feb 13, 2022 10:15 am
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
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