Question

6. Simplificați:

2 la puterea 41 + 4 la puterea 20 supra 8 la puterea 13 + 4 la puterea 20

Answer 1

Răspuns:

$\frac{2 {}^{41} + 4 {}^{20} }{8 {}^{13} + 4 {}^{20} } \\ \\ = \frac{2 {}^{41} + (2 {}^{2}) {}^{20} }{(2 {}^{3}) {}^{13} +4 {}^{20} } = \\ \\ = \frac{2 {}^{41} + 2 {}^{40} }{2 {}^{39} + 2 {}^{40} } = \\ \\ = \frac{(2 + 1) \times {2}^{40} }{(1 + 2) \times 2 {}^{39} } = \\ \\ = \frac{3 \times 2 {}^{40} }{3 \times 2 {}^{39} } = \\ \\ = \frac{3 \times 2}{3} = \\ \\ = \frac{6}{3} \\ \\ = 2$

Answer 2

Răspuns:

2⁴¹ + 4²⁰ / 8¹³ + 4²⁰

2⁴¹ + 2⁴⁰ / 8¹³ + 4²⁰

2⁴¹ + 2⁴⁰ / 2³⁹ / 4²⁰

2⁴¹ + 2⁴⁰ / 2³⁹ + 2⁴⁰

( 2 + 1 ) × 2⁴⁰ / 2³⁹ + 2⁴⁰

( 2× 1 ) × 2⁴⁰ / ( 1 × 2 ) × 2³⁹

3 × 2⁴⁰ / ( 1 × 2 ) × 2³⁹

3 × 2⁴⁰ / 3 × 2³⁹

3 × 2 / 3

2