Question

(UFPE) Simplificando $\sqrt[3]{ \frac{ 2^{31} + 2^{33} }{10} }$
obtemos:

Answer 1

Simplifique o seguinte:
(Sqrt (3) (2 ^ 31 + 2 ^ 33)) / (10)
2 ^ 2 = 2 (2 ^ 2) 2 = 2 (2 ^ 15) ^ 2 = 2 (2 × 2 ^ 14) 2 ^ 2) ^ 2 = 2 (2 (2 (2 ^ 3) ^ 2) ^ 2) ^ 2 = 2 (2 (2 (2 × 2 ^ 2)
(3) (2 (2 (2 (2x2 ^ 2) ^ 2) ^ 2 + 2 ^ 33)) / (10)
2 ^ 2 = 4:
(Sqrt (3) (2 (2 (2 (2 × 4) ^ 2) ^ 2) ^ 2 + 2 ^ 33)) / (10)
2 × 4 = 8:
(Sqrt (3) (2 (2 (2 × 8 ^ 2) ^ 2) ^ 2 + 2 ^ 33)) / (10)
8 ^ 2 = 64:
(Sqrt (3) (2 (2 (2 × 64) ^ 2) ^ 2 + 2 ^ 33)) / (10)
2 x 64 = 128:
(Sqrt (3) (2 (2 × 128 ^ 2) ^ 2 + 2 ^ 33)) / (10)
 | | 1 | 2 | 8
× | | 1 | 2 | 8
 | 1 | 0 | 2 | 4
 | 2 | 5 | 6 | 0
1 | 2 | 8 | 0 | 0
1 | 6 | 3 | 8 | 4:
(Sqrt (3) (2 (2 × 16384) ^ 2 + 2 ^ 33)) / (10)
2 × 16384 = 32768:
(Sqrt (3) (2 x 32768 ^ 2 + 2 ^ 33)) / (10)
 | | | | | 3 | 2 | 7 | 6 | 8
× | | | | | 3 | 2 | 7 | 6 | 8
 | | | | 2 | 6 | 2 | 1 | 4 | 4
 | | | 1 | 9 | 6 | 6 | 0 | 8 | 0
 | | 2 | 2 | 9 | 3 | 7 | 6 | 0 | 0
 | | 6 | 5 | 5 | 3 | 6 | 0 | 0 | 0
 | 9 | 8 | 3 | 0 | 4 | 0 | 0 | 0 | 0
1 | 0 | 7 | 3 | 7 | 4 | 1 | 8 | 2 | 4:
(Sqrt (3) (2 × 1073741824 + 2 ^ 33)) / (10)
2 × 1073741824 = 2147483648:
(Sqrt (3) (2147483648 + 2 ^ 33)) / (10)
2 ^ 33 = 2 × 2 ^ 32 = 2 (2 ^ 16) ^ 2 = 2 (2 ^ 8) ^ 2) ^ 2 = 2 ((2 ^ 4) ^ 2) ^ 2) ^ 2 = 2 ((((2 ^ 2) ^ 2) ^ 2) ^ 2) ^ 2:
(Sqrt (3) (2147483648 + 2 ((((2 ^ 2) ^ 2) ^ 2) ^ 2) ^ 2)) / (10)
2 ^ 2 = 4:
(Sqrt (3) (2147483648 + 2 (((4 ^ 2) ^ 2) ^ 2) ^ 2)) / (10)
4 ^ 2 = 16:
(Sqrt (3) (2147483648 + 2 ((16 ^ 2) ^ 2) ^ 2)) / (10)
 | 1 | 6
× | 1 | 6
 | 9 | 6
1 | 6 | 0
2 | 5 | 6:
(Sqrt (3) (2147483648 + 2 (256 ^ 2) ^ 2)) / (10)
 | | 2 | 5 | 6
× | | 2 | 5 | 6
 | 1 | 5 | 3 | 6
1 | 2 | 8 | 0 | 0
5 | 1 | 2 | 0 | 0
6 | 5 | 5 | 3 | 6:
(Sqrt (3) (2147483648 + 2 × 65536 ^ 2)) / (10)
 | | | | | 6 | 5 | 5 | 3 | 6
× | | | | | 6 | 5 | 5 | 3 | 6
 | | | | 3 | 9 | 3 | 2 | 1 | 6
 | | | 1 | 9 | 6 | 6 | 0 | 8 | 0
 | | 3 | 2 | 7 | 6 | 8 | 0 | 0 | 0
 | 3 | 2 | 7 | 6 | 8 | 0 | 0 | 0 | 0
3 | 9 | 3 | 2 | 1 | 6 | 0 | 0 | 0 | 0
4 | 2 | 9 | 4 | 9 | 6 | 7 | 2 | 9 | 6:
(Sqrt (3) (2147483648 + 2 × 4294967296)) / (10)
2 × 4294967296 = 8589934592:
(Sqrt (3) (2147483648 + 8589934592)) / (10)
2147483648 + 8589934592 = 10737418240:
(Sqrt (3) × 10737418240) / (10)
10737418240/10 = (10 x 1073741824) / 10 = 1073741824:
Resposta: |
 | 1073741824 sqrt (3)

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boa tarde!! :)

Answer 2

      $\sqrt[3]{ \frac{2^3^1+2^3^3}{10} } =$

Resolvendo o numerador:
  2³¹ + 2³³ = 2³¹ (1+2²) = 2³¹ . 5

Colocando o denominador:
  
$\frac{2^3^1 *5}{10} = \frac{2^3^1}{2} =2^3^1 : 2^1 = 2^3^0$

Então fica:
               $\sqrt[3]{2^3^0} = 2^1^0$