Question

Calculati:4 la puterea 14 - (6x4 la puterea 13 - 2x2la puterea 26)

Answer 1

${4}^{14} - (6 \times {4}^{13} - 2 \times {2}^{26}) = \\ \\ { {(2}^{2}) }^{14} - (6 \times { {(2}^{2}) }^{13} - 2 \times - {2}^{1} \times {2}^{26}) = \\ \\ {2}^{28} - (6 \times {2}^{26} - {2}^{1 + 26}) = \\ \\ {2}^{28} - (6 \times {2}^{26} - {2}^{27}) = \\ \\ {2}^{28} - (6 - 2) \times {2}^{26} = \\ \\ {2}^{28} - 4 \times {2}^{26} = \\ \\ ( {2}^{2} - 4) \times {2}^{26} = \\ \\ (4 - 4) \times {2}^{26} = \\ \\ 0 \times {2}^{26} = \\ \\ 0$

Answer 2

Răspuns

Explicație pas cu pas:

4¹⁴ - ( 6 x 4¹³ - 2 x 2²⁶ ) = 0

= ( 2² )¹⁴ - [ 3 x 2 x ( 2² )¹³ - 2 ⁽ ¹ ⁺ ²⁶ ⁾ ) =

= 2²⁸ - ( 3 x 2 ⁽ ¹ ⁺ ²⁶ ⁾  - 2²⁷ ) =

= 2²⁸ - 2²⁷ x ( 3 - 1 ) =

= 2²⁸ - 2²⁷ x 2 =

= 2 ²⁸ - 2²⁸ =

= 0