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

This topic has expert replies
Legendary Member
Posts: 2898
Joined: 07 Sep 2017
Thanked: 6 times
Followed by:5 members

Timer

00:00

Your Answer

A

B

C

D

E

Global Stats

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

Master | Next Rank: 500 Posts
Posts: 409
Joined: 15 Oct 2009
Thanked: 27 times
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