Question

(7^2004+7^2002+7^2003):57

Answer 1

Răspuns:

Explicație pas cu pas:

(7²⁰⁰⁴ + 7²⁰⁰²+7²⁰⁰³) : 57 =

= 7²⁰⁰²·(7²+7⁰+7¹) : 57 =

= 7²⁰⁰²·(49+1+7) : 57 =

= 7²⁰⁰²·57 : 57 = 7²⁰⁰²

Answer 2

 

$\displaystyle\bf\\\Big(7^{2004}+7^{2002}+7^{2003}\Big):57=~~~(adunarea~e~comutativa)\\\\\\=\Big(7^{2002}+7^{2003}+7^{2004}\Big):57=~~~(scriem~ca~fractie)\\\\\\=\frac{7^{2002}+7^{2003}+7^{2004}}{57}=\\\\\\=\frac{7^{2002}+7^{2002+1}+7^{2002+2}}{57}=\\\\\\=\frac{7^{2002}+7^{2002}\times7^1+7^{2002}\times7^2}{57}=~~~(Dam~factor~comun~pe~7^{2002})\\\\\\=\frac{7^{2002}\Big(1+7^1+7^2\Big)}{57}=\frac{7^{2002}\Big(1+7+49\Big)}{57}= \frac{7^{2002}\times57}{57}=\boxed{\bf7^{2002}}$