Answer:
Both terms have a common factor of 2^15
Step-by-step explanation:
Make use of prime factorizations:
16^5+2^15=(2^4)^5+2^15=2^20+2^15
Both terms have a common factor of 2^15.
16^5+2^15=2^15(2^5+1)=2^15 x 33
The term [tex]16^5+2^{15}[/tex] is divisible by 33
We have to given [tex]16^5+2^{15}[/tex] is divisible by 33.
Prime factorization is a way of expressing a number as a product of its prime factors
Make use of prime factorization
[tex]16^5+2^{15}=(2^4)^5+2^{15}[/tex]
[tex]=2^{20}+2^{15}[/tex]
factor out the term [tex]2^{15}[/tex] we get,
[tex]16^5+2^{15}=2^{15}(2^5+1)=2^{15} * 33[/tex]
Therefore the term [tex]16^5+2^{15}[/tex] is divisible by 33
Hence proved.
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