Question

Selesaikan
[tex]\displaystyle \frac{2^{2020}-2^{2016}-90}{2^{2015}-3}[/tex]

Answer 1

Verified answer

[tex]\begin{aligned}\frac{2^{2020}-2^{2016}-90}{2^{2015}-3}&=\,\boxed{\,\bf30\,}\end{aligned}[/tex]
 

Penjelasan dengan langkah-langkah:

[tex]\begin{aligned}&\frac{2^{2020}-2^{2016}-90}{2^{2015}-3}\\&{=\ }\frac{2^{2015}\left(2^5-2\right)-90}{2^{2015}-3}\\&{=\ }\frac{2^{2015}\cdot30-90}{2^{2015}-3}\\&{=\ }\frac{30\cancel{\left(2^{2015}-3\right)}}{\cancel{2^{2015}-3}}\\&{=\ }\boxed{\,\bf30\,}\end{aligned}[/tex]
[tex]\blacksquare[/tex]

Answer 2

Penyelesaian

[tex]\frac{2^{2020}-2^{2016}-90}{2^{2015}-3} \\ = \frac{ {2}^{2015 + 5} - {2}^{2015 + 1} - 90 }{ {2}^{2015} - 3 } \\ = \frac{ {2}^{2015} ( {2}^{5} - 2) - 90}{ {2}^{2015} - 3} \\ = \frac{ {2}^{2015}(32 - 2) - 90 }{ {2}^{2015} - 3} \\ = \frac{ {2}^{2015} (30) - 90}{ {2}^{2015} - 3 } \\ = \frac{ {2}^{2015} (30) - 3(30)}{ {2}^{2015} - 3 } \\ = \frac{30( {2}^{2015} - 3)}{ {2}^{2015} - 3 }[/tex]

=30

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