An algebra problem by Engin Akpinar

Algebra Level 1

2 666 × 2 − 374 = 2 y \Large{2^{666} × 2^{-374}=2^y} What is y \large y ?


The answer is 292.

Engin Akpinar by Engin Akpinar , 22, Canada

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3 solutions

Eric Taylor
May 31, 2017

According to exponent laws, when multiplying two numbers of the same base against each other you may add the exponents. Therefore...

2 666 × 2 − 374 = 2 666 + ( − 374 ) 2^{666}×2^{-374}=2^{666+(-374)}

2 666 × 2 − 374 = 2 292 2^{666}×2^{-374}=2^{292}

2 Helpful 0 Interesting 0 Brilliant 0 Confused
Mohammad Khaza
Jul 28, 2017

2 666 − 2 − 374 = 2 y 2^{666} -2^{-374} =2^y

or, 2 666 − 374 = 2 y 2^{666-374} =2^y

or, 2 292 = 2 y 2^{292}=2^y

or, 292 = y 292=y ..........................[removing the base]

1 Helpful 0 Interesting 0 Brilliant 0 Confused
Engin Akpinar
May 31, 2017

666 − 374 = 292 666-374 =292

2 292 2^{292}

1 Helpful 0 Interesting 0 Brilliant 0 Confused

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