If a^p = a^3t and a^t= a^5pr and p does not equal 0, then a= ?

Question

anonymous · Answer

answer choices:
1
2
3
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5

primeralph · Answer

Is this correct?
 a^5pr or is it  a^5p  ?

anonymous · Answer

Is this $a^p=a^{3t}$ and $a^t=a^{5p}$ ... ?

anonymous · Answer

$a$ could be either $0,1$

anonymous · Answer

it is a^t=a^(5pr)

anonymous · Answer

Assume $a\ne 0,1$ then we may equate exponents $p=3t,t=5p\implies t=15t$. $t=0$ therefore and so does $p$ -- we've reached a contradiction. Therefore $a=0$ or $a=1$

anonymous · Answer

what the hell is $r$?

anonymous · Answer

are there any conditions on $a,r$?

anonymous · Answer

If a^p = a^(3t) and a^t= a^(5pr) and p does not equal 0, then what is the value of r? @oldrin.bataku @primeralph  My bad!

anonymous · Answer

Are we told $a\ne0,1$? otherwise it could be literally anything

anonymous · Answer

well, any real number

anonymous · Answer

well, it says p doesn't equal zero, but that's it.

anonymous · Answer

If this is supposed to hold for any $a$ I suppose we could argue $r=1/15$ is a solution... see:$$a^p=a^{3t}\implies p=3t\a^t=a^{5pr}\implies t=5pr\t=5pr=3(5t)r=15tr\\frac1{15}=r$$